Prakalkulus Contoh

\frac{1}{1 + {log}_{c} (a b)} + \frac{1}{1 + {log}_{a} (b c)} + \frac{1}{1 + {log}_{b} (c a)}

$\frac{1}{1 + \log_{c} (a b)} + \frac{1}{1 + \log_{a} (b c)} + \frac{1}{1 + \log_{b} (c a)}$

Langkah 1

Tulis kembali

{log}_{c} (a b)

$\log_{c} (a b)$ sebagai

{log}_{c} (a) + {log}_{c} (b)

$\log_{c} (a) + \log_{c} (b)$ .

\frac{1}{1 + {log}_{c} (a) + {log}_{c} (b)} + \frac{1}{1 + {log}_{a} (b c)} + \frac{1}{1 + {log}_{b} (c a)}

$\frac{1}{1 + \log_{c} (a) + \log_{c} (b)} + \frac{1}{1 + \log_{a} (b c)} + \frac{1}{1 + \log_{b} (c a)}$

Langkah 2

Tulis kembali

{log}_{a} (b c)

$\log_{a} (b c)$ sebagai

{log}_{a} (b) + {log}_{a} (c)

$\log_{a} (b) + \log_{a} (c)$ .

\frac{1}{1 + {log}_{c} (a) + {log}_{c} (b)} + \frac{1}{1 + {log}_{a} (b) + {log}_{a} (c)} + \frac{1}{1 + {log}_{b} (c a)}

$\frac{1}{1 + \log_{c} (a) + \log_{c} (b)} + \frac{1}{1 + \log_{a} (b) + \log_{a} (c)} + \frac{1}{1 + \log_{b} (c a)}$

Langkah 3

Tulis kembali

{log}_{b} (c a)

$\log_{b} (c a)$ sebagai

{log}_{b} (c) + {log}_{b} (a)

$\log_{b} (c) + \log_{b} (a)$ .

\frac{1}{1 + {log}_{c} (a) + {log}_{c} (b)} + \frac{1}{1 + {log}_{a} (b) + {log}_{a} (c)} + \frac{1}{1 + {log}_{b} (c) + {log}_{b} (a)}

$\frac{1}{1 + \log_{c} (a) + \log_{c} (b)} + \frac{1}{1 + \log_{a} (b) + \log_{a} (c)} + \frac{1}{1 + \log_{b} (c) + \log_{b} (a)}$

Langkah 4

Untuk menuliskan

\frac{1}{1 + {log}_{c} (a) + {log}_{c} (b)}

$\frac{1}{1 + \log_{c} (a) + \log_{c} (b)}$ sebagai pecahan dengan penyebut umum, kalikan dengan

\frac{1 + {log}_{a} (b) + {log}_{a} (c)}{1 + {log}_{a} (b) + {log}_{a} (c)}

$\frac{1 + \log_{a} (b) + \log_{a} (c)}{1 + \log_{a} (b) + \log_{a} (c)}$ .

\frac{1}{1 + {log}_{c} (a) + {log}_{c} (b)} \cdot \frac{1 + {log}_{a} (b) + {log}_{a} (c)}{1 + {log}_{a} (b) + {log}_{a} (c)} + \frac{1}{1 + {log}_{a} (b) + {log}_{a} (c)} + \frac{1}{1 + {log}_{b} (c) + {log}_{b} (a)}

$\frac{1}{1 + \log_{c} (a) + \log_{c} (b)} \cdot \frac{1 + \log_{a} (b) + \log_{a} (c)}{1 + \log_{a} (b) + \log_{a} (c)} + \frac{1}{1 + \log_{a} (b) + \log_{a} (c)} + \frac{1}{1 + \log_{b} (c) + \log_{b} (a)}$

Langkah 5

Untuk menuliskan

\frac{1}{1 + {log}_{a} (b) + {log}_{a} (c)}

$\frac{1}{1 + \log_{a} (b) + \log_{a} (c)}$ sebagai pecahan dengan penyebut umum, kalikan dengan

\frac{1 + {log}_{c} (a) + {log}_{c} (b)}{1 + {log}_{c} (a) + {log}_{c} (b)}

$\frac{1 + \log_{c} (a) + \log_{c} (b)}{1 + \log_{c} (a) + \log_{c} (b)}$ .

\frac{1}{1 + {log}_{c} (a) + {log}_{c} (b)} \cdot \frac{1 + {log}_{a} (b) + {log}_{a} (c)}{1 + {log}_{a} (b) + {log}_{a} (c)} + \frac{1}{1 + {log}_{a} (b) + {log}_{a} (c)} \cdot \frac{1 + {log}_{c} (a) + {log}_{c} (b)}{1 + {log}_{c} (a) + {log}_{c} (b)} + \frac{1}{1 + {log}_{b} (c) + {log}_{b} (a)}

$\frac{1}{1 + \log_{c} (a) + \log_{c} (b)} \cdot \frac{1 + \log_{a} (b) + \log_{a} (c)}{1 + \log_{a} (b) + \log_{a} (c)} + \frac{1}{1 + \log_{a} (b) + \log_{a} (c)} \cdot \frac{1 + \log_{c} (a) + \log_{c} (b)}{1 + \log_{c} (a) + \log_{c} (b)} + \frac{1}{1 + \log_{b} (c) + \log_{b} (a)}$

Langkah 6

Tulis setiap pernyataan menggunakan penyebut umum dari

(1 + {log}_{c} (a) + {log}_{c} (b)) (1 + {log}_{a} (b) + {log}_{a} (c))

$(1 + \log_{c} (a) + \log_{c} (b)) (1 + \log_{a} (b) + \log_{a} (c))$ , dengan mengalikan masing-masing pembilang dan penyebut dengan faktor dari

1

$1$ yang sesuai.

Ketuk untuk lebih banyak langkah...

Langkah 6.1

Kalikan

\frac{1}{1 + {log}_{c} (a) + {log}_{c} (b)}

$\frac{1}{1 + \log_{c} (a) + \log_{c} (b)}$ dengan

\frac{1 + {log}_{a} (b) + {log}_{a} (c)}{1 + {log}_{a} (b) + {log}_{a} (c)}

$\frac{1 + \log_{a} (b) + \log_{a} (c)}{1 + \log_{a} (b) + \log_{a} (c)}$ .

\frac{1 + {log}_{a} (b) + {log}_{a} (c)}{(1 + {log}_{c} (a) + {log}_{c} (b)) (1 + {log}_{a} (b) + {log}_{a} (c))} + \frac{1}{1 + {log}_{a} (b) + {log}_{a} (c)} \cdot \frac{1 + {log}_{c} (a) + {log}_{c} (b)}{1 + {log}_{c} (a) + {log}_{c} (b)} + \frac{1}{1 + {log}_{b} (c) + {log}_{b} (a)}

$\frac{1 + \log_{a} (b) + \log_{a} (c)}{(1 + \log_{c} (a) + \log_{c} (b)) (1 + \log_{a} (b) + \log_{a} (c))} + \frac{1}{1 + \log_{a} (b) + \log_{a} (c)} \cdot \frac{1 + \log_{c} (a) + \log_{c} (b)}{1 + \log_{c} (a) + \log_{c} (b)} + \frac{1}{1 + \log_{b} (c) + \log_{b} (a)}$

Langkah 6.2

Kalikan

\frac{1}{1 + {log}_{a} (b) + {log}_{a} (c)}

$\frac{1}{1 + \log_{a} (b) + \log_{a} (c)}$ dengan

\frac{1 + {log}_{c} (a) + {log}_{c} (b)}{1 + {log}_{c} (a) + {log}_{c} (b)}

$\frac{1 + \log_{c} (a) + \log_{c} (b)}{1 + \log_{c} (a) + \log_{c} (b)}$ .

\frac{1 + {log}_{a} (b) + {log}_{a} (c)}{(1 + {log}_{c} (a) + {log}_{c} (b)) (1 + {log}_{a} (b) + {log}_{a} (c))} + \frac{1 + {log}_{c} (a) + {log}_{c} (b)}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))} + \frac{1}{1 + {log}_{b} (c) + {log}_{b} (a)}

$\frac{1 + \log_{a} (b) + \log_{a} (c)}{(1 + \log_{c} (a) + \log_{c} (b)) (1 + \log_{a} (b) + \log_{a} (c))} + \frac{1 + \log_{c} (a) + \log_{c} (b)}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))} + \frac{1}{1 + \log_{b} (c) + \log_{b} (a)}$

Langkah 6.3

Susun kembali faktor-faktor dari

(1 + {log}_{c} (a) + {log}_{c} (b)) (1 + {log}_{a} (b) + {log}_{a} (c))

$(1 + \log_{c} (a) + \log_{c} (b)) (1 + \log_{a} (b) + \log_{a} (c))$ .

\frac{1 + {log}_{a} (b) + {log}_{a} (c)}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))} + \frac{1 + {log}_{c} (a) + {log}_{c} (b)}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))} + \frac{1}{1 + {log}_{b} (c) + {log}_{b} (a)}

$\frac{1 + \log_{a} (b) + \log_{a} (c)}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))} + \frac{1 + \log_{c} (a) + \log_{c} (b)}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))} + \frac{1}{1 + \log_{b} (c) + \log_{b} (a)}$

\frac{1 + {log}_{a} (b) + {log}_{a} (c)}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))} + \frac{1 + {log}_{c} (a) + {log}_{c} (b)}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))} + \frac{1}{1 + {log}_{b} (c) + {log}_{b} (a)}

Langkah 7

Gabungkan pembilang dari penyebut persekutuan.

\frac{1 + {log}_{a} (b) + {log}_{a} (c) + 1 + {log}_{c} (a) + {log}_{c} (b)}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))} + \frac{1}{1 + {log}_{b} (c) + {log}_{b} (a)}

$\frac{1 + \log_{a} (b) + \log_{a} (c) + 1 + \log_{c} (a) + \log_{c} (b)}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))} + \frac{1}{1 + \log_{b} (c) + \log_{b} (a)}$

Langkah 8

Tambahkan

1

$1$ dan

1

$1$ .

\frac{2 + {log}_{a} (b) + {log}_{a} (c) + {log}_{c} (a) + {log}_{c} (b)}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))} + \frac{1}{1 + {log}_{b} (c) + {log}_{b} (a)}

$\frac{2 + \log_{a} (b) + \log_{a} (c) + \log_{c} (a) + \log_{c} (b)}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))} + \frac{1}{1 + \log_{b} (c) + \log_{b} (a)}$

Langkah 9

Untuk menuliskan

\frac{2 + {log}_{a} (b) + {log}_{a} (c) + {log}_{c} (a) + {log}_{c} (b)}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))}

$\frac{2 + \log_{a} (b) + \log_{a} (c) + \log_{c} (a) + \log_{c} (b)}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))}$ sebagai pecahan dengan penyebut umum, kalikan dengan

\frac{1 + {log}_{b} (c) + {log}_{b} (a)}{1 + {log}_{b} (c) + {log}_{b} (a)}

$\frac{1 + \log_{b} (c) + \log_{b} (a)}{1 + \log_{b} (c) + \log_{b} (a)}$ .

\frac{2 + {log}_{a} (b) + {log}_{a} (c) + {log}_{c} (a) + {log}_{c} (b)}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))} \cdot \frac{1 + {log}_{b} (c) + {log}_{b} (a)}{1 + {log}_{b} (c) + {log}_{b} (a)} + \frac{1}{1 + {log}_{b} (c) + {log}_{b} (a)}

Langkah 10

Untuk menuliskan

\frac{1}{1 + {log}_{b} (c) + {log}_{b} (a)}

$\frac{1}{1 + \log_{b} (c) + \log_{b} (a)}$ sebagai pecahan dengan penyebut umum, kalikan dengan

\frac{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))}

$\frac{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))}$ .

\frac{2 + {log}_{a} (b) + {log}_{a} (c) + {log}_{c} (a) + {log}_{c} (b)}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))} \cdot \frac{1 + {log}_{b} (c) + {log}_{b} (a)}{1 + {log}_{b} (c) + {log}_{b} (a)} + \frac{1}{1 + {log}_{b} (c) + {log}_{b} (a)} \cdot \frac{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))}

$\frac{2 + \log_{a} (b) + \log_{a} (c) + \log_{c} (a) + \log_{c} (b)}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))} \cdot \frac{1 + \log_{b} (c) + \log_{b} (a)}{1 + \log_{b} (c) + \log_{b} (a)} + \frac{1}{1 + \log_{b} (c) + \log_{b} (a)} \cdot \frac{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))}$

Langkah 11

Tulis setiap pernyataan menggunakan penyebut umum dari

(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b)) (1 + {log}_{b} (c) + {log}_{b} (a))

$(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b)) (1 + \log_{b} (c) + \log_{b} (a))$ , dengan mengalikan masing-masing pembilang dan penyebut dengan faktor dari

1

$1$ yang sesuai.

Ketuk untuk lebih banyak langkah...

Langkah 11.1

Kalikan

\frac{2 + {log}_{a} (b) + {log}_{a} (c) + {log}_{c} (a) + {log}_{c} (b)}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))}

$\frac{2 + \log_{a} (b) + \log_{a} (c) + \log_{c} (a) + \log_{c} (b)}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))}$ dengan

\frac{1 + {log}_{b} (c) + {log}_{b} (a)}{1 + {log}_{b} (c) + {log}_{b} (a)}

$\frac{1 + \log_{b} (c) + \log_{b} (a)}{1 + \log_{b} (c) + \log_{b} (a)}$ .

\frac{(2 + {log}_{a} (b) + {log}_{a} (c) + {log}_{c} (a) + {log}_{c} (b)) (1 + {log}_{b} (c) + {log}_{b} (a))}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b)) (1 + {log}_{b} (c) + {log}_{b} (a))} + \frac{1}{1 + {log}_{b} (c) + {log}_{b} (a)} \cdot \frac{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))}

$\frac{(2 + \log_{a} (b) + \log_{a} (c) + \log_{c} (a) + \log_{c} (b)) (1 + \log_{b} (c) + \log_{b} (a))}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b)) (1 + \log_{b} (c) + \log_{b} (a))} + \frac{1}{1 + \log_{b} (c) + \log_{b} (a)} \cdot \frac{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))}$

Langkah 11.2

Kalikan

\frac{1}{1 + {log}_{b} (c) + {log}_{b} (a)}

$\frac{1}{1 + \log_{b} (c) + \log_{b} (a)}$ dengan

\frac{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))}

$\frac{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))}$ .

\frac{(2 + {log}_{a} (b) + {log}_{a} (c) + {log}_{c} (a) + {log}_{c} (b)) (1 + {log}_{b} (c) + {log}_{b} (a))}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b)) (1 + {log}_{b} (c) + {log}_{b} (a))} + \frac{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))}{(1 + {log}_{b} (c) + {log}_{b} (a)) ((1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b)))}

$\frac{(2 + \log_{a} (b) + \log_{a} (c) + \log_{c} (a) + \log_{c} (b)) (1 + \log_{b} (c) + \log_{b} (a))}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b)) (1 + \log_{b} (c) + \log_{b} (a))} + \frac{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))}{(1 + \log_{b} (c) + \log_{b} (a)) ((1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b)))}$

Langkah 11.3

Susun kembali faktor-faktor dari

(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b)) (1 + {log}_{b} (c) + {log}_{b} (a))

$(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b)) (1 + \log_{b} (c) + \log_{b} (a))$ .

\frac{(2 + {log}_{a} (b) + {log}_{a} (c) + {log}_{c} (a) + {log}_{c} (b)) (1 + {log}_{b} (c) + {log}_{b} (a))}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{b} (c) + {log}_{b} (a)) (1 + {log}_{c} (a) + {log}_{c} (b))} + \frac{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))}{(1 + {log}_{b} (c) + {log}_{b} (a)) ((1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b)))}

$\frac{(2 + \log_{a} (b) + \log_{a} (c) + \log_{c} (a) + \log_{c} (b)) (1 + \log_{b} (c) + \log_{b} (a))}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{b} (c) + \log_{b} (a)) (1 + \log_{c} (a) + \log_{c} (b))} + \frac{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))}{(1 + \log_{b} (c) + \log_{b} (a)) ((1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b)))}$

Langkah 11.4

Susun kembali faktor-faktor dari

(1 + {log}_{b} (c) + {log}_{b} (a)) ((1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b)))

$(1 + \log_{b} (c) + \log_{b} (a)) ((1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b)))$ .

\frac{(2 + {log}_{a} (b) + {log}_{a} (c) + {log}_{c} (a) + {log}_{c} (b)) (1 + {log}_{b} (c) + {log}_{b} (a))}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{b} (c) + {log}_{b} (a)) (1 + {log}_{c} (a) + {log}_{c} (b))} + \frac{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{b} (c) + {log}_{b} (a)) (1 + {log}_{c} (a) + {log}_{c} (b))}

$\frac{(2 + \log_{a} (b) + \log_{a} (c) + \log_{c} (a) + \log_{c} (b)) (1 + \log_{b} (c) + \log_{b} (a))}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{b} (c) + \log_{b} (a)) (1 + \log_{c} (a) + \log_{c} (b))} + \frac{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{b} (c) + \log_{b} (a)) (1 + \log_{c} (a) + \log_{c} (b))}$

\frac{(2 + {log}_{a} (b) + {log}_{a} (c) + {log}_{c} (a) + {log}_{c} (b)) (1 + {log}_{b} (c) + {log}_{b} (a))}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{b} (c) + {log}_{b} (a)) (1 + {log}_{c} (a) + {log}_{c} (b))} + \frac{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{b} (c) + {log}_{b} (a)) (1 + {log}_{c} (a) + {log}_{c} (b))}

$\frac{(2 + \log_{a} (b) + \log_{a} (c) + \log_{c} (a) + \log_{c} (b)) (1 + \log_{b} (c) + \log_{b} (a))}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{b} (c) + \log_{b} (a)) (1 + \log_{c} (a) + \log_{c} (b))} + \frac{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{b} (c) + \log_{b} (a)) (1 + \log_{c} (a) + \log_{c} (b))}$

Langkah 12

Gabungkan pembilang dari penyebut persekutuan.

\frac{(2 + {log}_{a} (b) + {log}_{a} (c) + {log}_{c} (a) + {log}_{c} (b)) (1 + {log}_{b} (c) + {log}_{b} (a)) + (1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{b} (c) + {log}_{b} (a)) (1 + {log}_{c} (a) + {log}_{c} (b))}

$\frac{(2 + \log_{a} (b) + \log_{a} (c) + \log_{c} (a) + \log_{c} (b)) (1 + \log_{b} (c) + \log_{b} (a)) + (1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{b} (c) + \log_{b} (a)) (1 + \log_{c} (a) + \log_{c} (b))}$

Langkah 13

Sederhanakan pembilangnya.

Ketuk untuk lebih banyak langkah...

Langkah 13.1

Perluas

(2 + {log}_{a} (b) + {log}_{a} (c) + {log}_{c} (a) + {log}_{c} (b)) (1 + {log}_{b} (c) + {log}_{b} (a))

$(2 + \log_{a} (b) + \log_{a} (c) + \log_{c} (a) + \log_{c} (b)) (1 + \log_{b} (c) + \log_{b} (a))$ dengan mengalikan setiap suku dalam pernyataan pertama dengan setiap suku dalam pernyataan kedua.

\frac{2 \cdot 1 + 2 {log}_{b} (c) + 2 {log}_{b} (a) + {log}_{a} (b) \cdot 1 + {log}_{a} (b) {log}_{b} (c) + {log}_{a} (b) {log}_{b} (a) + {log}_{a} (c) \cdot 1 + {log}_{a} (c) {log}_{b} (c) + {log}_{a} (c) {log}_{b} (a) + {log}_{c} (a) \cdot 1 + {log}_{c} (a) {log}_{b} (c) + {log}_{c} (a) {log}_{b} (a) + {log}_{c} (b) \cdot 1 + {log}_{c} (b) {log}_{b} (c) + {log}_{c} (b) {log}_{b} (a) + (1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{b} (c) + {log}_{b} (a)) (1 + {log}_{c} (a) + {log}_{c} (b))}

$\frac{2 \cdot 1 + 2 \log_{b} (c) + 2 \log_{b} (a) + \log_{a} (b) \cdot 1 + \log_{a} (b) \log_{b} (c) + \log_{a} (b) \log_{b} (a) + \log_{a} (c) \cdot 1 + \log_{a} (c) \log_{b} (c) + \log_{a} (c) \log_{b} (a) + \log_{c} (a) \cdot 1 + \log_{c} (a) \log_{b} (c) + \log_{c} (a) \log_{b} (a) + \log_{c} (b) \cdot 1 + \log_{c} (b) \log_{b} (c) + \log_{c} (b) \log_{b} (a) + (1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{b} (c) + \log_{b} (a)) (1 + \log_{c} (a) + \log_{c} (b))}$

Langkah 13.2

Sederhanakan setiap suku.

Ketuk untuk lebih banyak langkah...

Langkah 13.2.1

Kalikan

2

$2$ dengan

1

$1$ .

\frac{2 + 2 {log}_{b} (c) + 2 {log}_{b} (a) + {log}_{a} (b) \cdot 1 + {log}_{a} (b) {log}_{b} (c) + {log}_{a} (b) {log}_{b} (a) + {log}_{a} (c) \cdot 1 + {log}_{a} (c) {log}_{b} (c) + {log}_{a} (c) {log}_{b} (a) + {log}_{c} (a) \cdot 1 + {log}_{c} (a) {log}_{b} (c) + {log}_{c} (a) {log}_{b} (a) + {log}_{c} (b) \cdot 1 + {log}_{c} (b) {log}_{b} (c) + {log}_{c} (b) {log}_{b} (a) + (1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{b} (c) + {log}_{b} (a)) (1 + {log}_{c} (a) + {log}_{c} (b))}

$\frac{2 + 2 \log_{b} (c) + 2 \log_{b} (a) + \log_{a} (b) \cdot 1 + \log_{a} (b) \log_{b} (c) + \log_{a} (b) \log_{b} (a) + \log_{a} (c) \cdot 1 + \log_{a} (c) \log_{b} (c) + \log_{a} (c) \log_{b} (a) + \log_{c} (a) \cdot 1 + \log_{c} (a) \log_{b} (c) + \log_{c} (a) \log_{b} (a) + \log_{c} (b) \cdot 1 + \log_{c} (b) \log_{b} (c) + \log_{c} (b) \log_{b} (a) + (1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{b} (c) + \log_{b} (a)) (1 + \log_{c} (a) + \log_{c} (b))}$

Langkah 13.2.2

Kalikan

{log}_{a} (b)

$\log_{a} (b)$ dengan

1

$1$ .

\frac{2 + 2 {log}_{b} (c) + 2 {log}_{b} (a) + {log}_{a} (b) + {log}_{a} (b) {log}_{b} (c) + {log}_{a} (b) {log}_{b} (a) + {log}_{a} (c) \cdot 1 + {log}_{a} (c) {log}_{b} (c) + {log}_{a} (c) {log}_{b} (a) + {log}_{c} (a) \cdot 1 + {log}_{c} (a) {log}_{b} (c) + {log}_{c} (a) {log}_{b} (a) + {log}_{c} (b) \cdot 1 + {log}_{c} (b) {log}_{b} (c) + {log}_{c} (b) {log}_{b} (a) + (1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{b} (c) + {log}_{b} (a)) (1 + {log}_{c} (a) + {log}_{c} (b))}

$\frac{2 + 2 \log_{b} (c) + 2 \log_{b} (a) + \log_{a} (b) + \log_{a} (b) \log_{b} (c) + \log_{a} (b) \log_{b} (a) + \log_{a} (c) \cdot 1 + \log_{a} (c) \log_{b} (c) + \log_{a} (c) \log_{b} (a) + \log_{c} (a) \cdot 1 + \log_{c} (a) \log_{b} (c) + \log_{c} (a) \log_{b} (a) + \log_{c} (b) \cdot 1 + \log_{c} (b) \log_{b} (c) + \log_{c} (b) \log_{b} (a) + (1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{b} (c) + \log_{b} (a)) (1 + \log_{c} (a) + \log_{c} (b))}$

Langkah 13.2.3

Kalikan

{log}_{a} (c)

$\log_{a} (c)$ dengan

1

$1$ .

\frac{2 + 2 {log}_{b} (c) + 2 {log}_{b} (a) + {log}_{a} (b) + {log}_{a} (b) {log}_{b} (c) + {log}_{a} (b) {log}_{b} (a) + {log}_{a} (c) + {log}_{a} (c) {log}_{b} (c) + {log}_{a} (c) {log}_{b} (a) + {log}_{c} (a) \cdot 1 + {log}_{c} (a) {log}_{b} (c) + {log}_{c} (a) {log}_{b} (a) + {log}_{c} (b) \cdot 1 + {log}_{c} (b) {log}_{b} (c) + {log}_{c} (b) {log}_{b} (a) + (1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{c} (a) + {log}_{c} (b))}{(1 + {log}_{a} (b) + {log}_{a} (c)) (1 + {log}_{b} (c) + {log}_{b} (a)) (1 + {log}_{c} (a) + {log}_{c} (b))}

$\frac{2 + 2 \log_{b} (c) + 2 \log_{b} (a) + \log_{a} (b) + \log_{a} (b) \log_{b} (c) + \log_{a} (b) \log_{b} (a) + \log_{a} (c) + \log_{a} (c) \log_{b} (c) + \log_{a} (c) \log_{b} (a) + \log_{c} (a) \cdot 1 + \log_{c} (a) \log_{b} (c) + \log_{c} (a) \log_{b} (a) + \log_{c} (b) \cdot 1 + \log_{c} (b) \log_{b} (c) + \log_{c} (b) \log_{b} (a) + (1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{b} (c) + \log_{b} (a)) (1 + \log_{c} (a) + \log_{c} (b))}$

Langkah 13.2.4

Kalikan

$\log_{c} (a)$ dengan

$1$ .

$\frac{2 + 2 \log_{b} (c) + 2 \log_{b} (a) + \log_{a} (b) + \log_{a} (b) \log_{b} (c) + \log_{a} (b) \log_{b} (a) + \log_{a} (c) + \log_{a} (c) \log_{b} (c) + \log_{a} (c) \log_{b} (a) + \log_{c} (a) + \log_{c} (a) \log_{b} (c) + \log_{c} (a) \log_{b} (a) + \log_{c} (b) \cdot 1 + \log_{c} (b) \log_{b} (c) + \log_{c} (b) \log_{b} (a) + (1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{b} (c) + \log_{b} (a)) (1 + \log_{c} (a) + \log_{c} (b))}$

Langkah 13.2.5

Kalikan

$\log_{c} (b)$ dengan

$1$ .

$\frac{2 + 2 \log_{b} (c) + 2 \log_{b} (a) + \log_{a} (b) + \log_{a} (b) \log_{b} (c) + \log_{a} (b) \log_{b} (a) + \log_{a} (c) + \log_{a} (c) \log_{b} (c) + \log_{a} (c) \log_{b} (a) + \log_{c} (a) + \log_{c} (a) \log_{b} (c) + \log_{c} (a) \log_{b} (a) + \log_{c} (b) + \log_{c} (b) \log_{b} (c) + \log_{c} (b) \log_{b} (a) + (1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{b} (c) + \log_{b} (a)) (1 + \log_{c} (a) + \log_{c} (b))}$

Langkah 13.3

Perluas

$(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{c} (a) + \log_{c} (b))$ dengan mengalikan setiap suku dalam pernyataan pertama dengan setiap suku dalam pernyataan kedua.

$\frac{2 + 2 \log_{b} (c) + 2 \log_{b} (a) + \log_{a} (b) + \log_{a} (b) \log_{b} (c) + \log_{a} (b) \log_{b} (a) + \log_{a} (c) + \log_{a} (c) \log_{b} (c) + \log_{a} (c) \log_{b} (a) + \log_{c} (a) + \log_{c} (a) \log_{b} (c) + \log_{c} (a) \log_{b} (a) + \log_{c} (b) + \log_{c} (b) \log_{b} (c) + \log_{c} (b) \log_{b} (a) + 1 \cdot 1 + 1 \log_{c} (a) + 1 \log_{c} (b) + \log_{a} (b) \cdot 1 + \log_{a} (b) \log_{c} (a) + \log_{a} (b) \log_{c} (b) + \log_{a} (c) \cdot 1 + \log_{a} (c) \log_{c} (a) + \log_{a} (c) \log_{c} (b)}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{b} (c) + \log_{b} (a)) (1 + \log_{c} (a) + \log_{c} (b))}$

Langkah 13.4

Sederhanakan setiap suku.

Ketuk untuk lebih banyak langkah...

Langkah 13.4.1

Kalikan

$1$ dengan

$1$ .

$\frac{2 + 2 \log_{b} (c) + 2 \log_{b} (a) + \log_{a} (b) + \log_{a} (b) \log_{b} (c) + \log_{a} (b) \log_{b} (a) + \log_{a} (c) + \log_{a} (c) \log_{b} (c) + \log_{a} (c) \log_{b} (a) + \log_{c} (a) + \log_{c} (a) \log_{b} (c) + \log_{c} (a) \log_{b} (a) + \log_{c} (b) + \log_{c} (b) \log_{b} (c) + \log_{c} (b) \log_{b} (a) + 1 + 1 \log_{c} (a) + 1 \log_{c} (b) + \log_{a} (b) \cdot 1 + \log_{a} (b) \log_{c} (a) + \log_{a} (b) \log_{c} (b) + \log_{a} (c) \cdot 1 + \log_{a} (c) \log_{c} (a) + \log_{a} (c) \log_{c} (b)}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{b} (c) + \log_{b} (a)) (1 + \log_{c} (a) + \log_{c} (b))}$

Langkah 13.4.2

Kalikan

$\log_{c} (a)$ dengan

$1$ .

$\frac{2 + 2 \log_{b} (c) + 2 \log_{b} (a) + \log_{a} (b) + \log_{a} (b) \log_{b} (c) + \log_{a} (b) \log_{b} (a) + \log_{a} (c) + \log_{a} (c) \log_{b} (c) + \log_{a} (c) \log_{b} (a) + \log_{c} (a) + \log_{c} (a) \log_{b} (c) + \log_{c} (a) \log_{b} (a) + \log_{c} (b) + \log_{c} (b) \log_{b} (c) + \log_{c} (b) \log_{b} (a) + 1 + \log_{c} (a) + 1 \log_{c} (b) + \log_{a} (b) \cdot 1 + \log_{a} (b) \log_{c} (a) + \log_{a} (b) \log_{c} (b) + \log_{a} (c) \cdot 1 + \log_{a} (c) \log_{c} (a) + \log_{a} (c) \log_{c} (b)}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{b} (c) + \log_{b} (a)) (1 + \log_{c} (a) + \log_{c} (b))}$

Langkah 13.4.3

Kalikan

$\log_{c} (b)$ dengan

$1$ .

$\frac{2 + 2 \log_{b} (c) + 2 \log_{b} (a) + \log_{a} (b) + \log_{a} (b) \log_{b} (c) + \log_{a} (b) \log_{b} (a) + \log_{a} (c) + \log_{a} (c) \log_{b} (c) + \log_{a} (c) \log_{b} (a) + \log_{c} (a) + \log_{c} (a) \log_{b} (c) + \log_{c} (a) \log_{b} (a) + \log_{c} (b) + \log_{c} (b) \log_{b} (c) + \log_{c} (b) \log_{b} (a) + 1 + \log_{c} (a) + \log_{c} (b) + \log_{a} (b) \cdot 1 + \log_{a} (b) \log_{c} (a) + \log_{a} (b) \log_{c} (b) + \log_{a} (c) \cdot 1 + \log_{a} (c) \log_{c} (a) + \log_{a} (c) \log_{c} (b)}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{b} (c) + \log_{b} (a)) (1 + \log_{c} (a) + \log_{c} (b))}$

Langkah 13.4.4

Kalikan

$\log_{a} (b)$ dengan

$1$ .

$\frac{2 + 2 \log_{b} (c) + 2 \log_{b} (a) + \log_{a} (b) + \log_{a} (b) \log_{b} (c) + \log_{a} (b) \log_{b} (a) + \log_{a} (c) + \log_{a} (c) \log_{b} (c) + \log_{a} (c) \log_{b} (a) + \log_{c} (a) + \log_{c} (a) \log_{b} (c) + \log_{c} (a) \log_{b} (a) + \log_{c} (b) + \log_{c} (b) \log_{b} (c) + \log_{c} (b) \log_{b} (a) + 1 + \log_{c} (a) + \log_{c} (b) + \log_{a} (b) + \log_{a} (b) \log_{c} (a) + \log_{a} (b) \log_{c} (b) + \log_{a} (c) \cdot 1 + \log_{a} (c) \log_{c} (a) + \log_{a} (c) \log_{c} (b)}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{b} (c) + \log_{b} (a)) (1 + \log_{c} (a) + \log_{c} (b))}$

Langkah 13.4.5

Kalikan

$\log_{a} (c)$ dengan

$1$ .

$\frac{2 + 2 \log_{b} (c) + 2 \log_{b} (a) + \log_{a} (b) + \log_{a} (b) \log_{b} (c) + \log_{a} (b) \log_{b} (a) + \log_{a} (c) + \log_{a} (c) \log_{b} (c) + \log_{a} (c) \log_{b} (a) + \log_{c} (a) + \log_{c} (a) \log_{b} (c) + \log_{c} (a) \log_{b} (a) + \log_{c} (b) + \log_{c} (b) \log_{b} (c) + \log_{c} (b) \log_{b} (a) + 1 + \log_{c} (a) + \log_{c} (b) + \log_{a} (b) + \log_{a} (b) \log_{c} (a) + \log_{a} (b) \log_{c} (b) + \log_{a} (c) + \log_{a} (c) \log_{c} (a) + \log_{a} (c) \log_{c} (b)}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{b} (c) + \log_{b} (a)) (1 + \log_{c} (a) + \log_{c} (b))}$

Langkah 13.5

Tambahkan

$2$ dan

$1$ .

$\frac{2 \log_{b} (c) + 2 \log_{b} (a) + \log_{a} (b) + \log_{a} (b) \log_{b} (c) + \log_{a} (b) \log_{b} (a) + \log_{a} (c) + \log_{a} (c) \log_{b} (c) + \log_{a} (c) \log_{b} (a) + \log_{c} (a) + \log_{c} (a) \log_{b} (c) + \log_{c} (a) \log_{b} (a) + \log_{c} (b) + \log_{c} (b) \log_{b} (c) + \log_{c} (b) \log_{b} (a) + 3 + \log_{c} (a) + \log_{c} (b) + \log_{a} (b) + \log_{a} (b) \log_{c} (a) + \log_{a} (b) \log_{c} (b) + \log_{a} (c) + \log_{a} (c) \log_{c} (a) + \log_{a} (c) \log_{c} (b)}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{b} (c) + \log_{b} (a)) (1 + \log_{c} (a) + \log_{c} (b))}$

Langkah 13.6

Tambahkan

$\log_{a} (b)$ dan

$\log_{a} (b)$ .

$\frac{2 \log_{b} (c) + 2 \log_{b} (a) + \log_{a} (b) \log_{b} (c) + \log_{a} (b) \log_{b} (a) + \log_{a} (c) + \log_{a} (c) \log_{b} (c) + \log_{a} (c) \log_{b} (a) + \log_{c} (a) + \log_{c} (a) \log_{b} (c) + \log_{c} (a) \log_{b} (a) + \log_{c} (b) + \log_{c} (b) \log_{b} (c) + \log_{c} (b) \log_{b} (a) + 3 + \log_{c} (a) + \log_{c} (b) + 2 \log_{a} (b) + \log_{a} (b) \log_{c} (a) + \log_{a} (b) \log_{c} (b) + \log_{a} (c) + \log_{a} (c) \log_{c} (a) + \log_{a} (c) \log_{c} (b)}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{b} (c) + \log_{b} (a)) (1 + \log_{c} (a) + \log_{c} (b))}$

Langkah 13.7

Tambahkan

$\log_{a} (c)$ dan

$\log_{a} (c)$ .

$\frac{2 \log_{b} (c) + 2 \log_{b} (a) + \log_{a} (b) \log_{b} (c) + \log_{a} (b) \log_{b} (a) + \log_{a} (c) \log_{b} (c) + \log_{a} (c) \log_{b} (a) + \log_{c} (a) + \log_{c} (a) \log_{b} (c) + \log_{c} (a) \log_{b} (a) + \log_{c} (b) + \log_{c} (b) \log_{b} (c) + \log_{c} (b) \log_{b} (a) + 3 + \log_{c} (a) + \log_{c} (b) + 2 \log_{a} (b) + \log_{a} (b) \log_{c} (a) + \log_{a} (b) \log_{c} (b) + 2 \log_{a} (c) + \log_{a} (c) \log_{c} (a) + \log_{a} (c) \log_{c} (b)}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{b} (c) + \log_{b} (a)) (1 + \log_{c} (a) + \log_{c} (b))}$

Langkah 13.8

Tambahkan

$\log_{c} (a)$ dan

$\log_{c} (a)$ .

$\frac{2 \log_{b} (c) + 2 \log_{b} (a) + \log_{a} (b) \log_{b} (c) + \log_{a} (b) \log_{b} (a) + \log_{a} (c) \log_{b} (c) + \log_{a} (c) \log_{b} (a) + \log_{c} (a) \log_{b} (c) + \log_{c} (a) \log_{b} (a) + \log_{c} (b) + \log_{c} (b) \log_{b} (c) + \log_{c} (b) \log_{b} (a) + 3 + 2 \log_{c} (a) + \log_{c} (b) + 2 \log_{a} (b) + \log_{a} (b) \log_{c} (a) + \log_{a} (b) \log_{c} (b) + 2 \log_{a} (c) + \log_{a} (c) \log_{c} (a) + \log_{a} (c) \log_{c} (b)}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{b} (c) + \log_{b} (a)) (1 + \log_{c} (a) + \log_{c} (b))}$

Langkah 13.9

Tambahkan

$\log_{c} (b)$ dan

$\log_{c} (b)$ .

$\frac{2 \log_{b} (c) + 2 \log_{b} (a) + \log_{a} (b) \log_{b} (c) + \log_{a} (b) \log_{b} (a) + \log_{a} (c) \log_{b} (c) + \log_{a} (c) \log_{b} (a) + \log_{c} (a) \log_{b} (c) + \log_{c} (a) \log_{b} (a) + \log_{c} (b) \log_{b} (c) + \log_{c} (b) \log_{b} (a) + 3 + 2 \log_{c} (a) + 2 \log_{c} (b) + 2 \log_{a} (b) + \log_{a} (b) \log_{c} (a) + \log_{a} (b) \log_{c} (b) + 2 \log_{a} (c) + \log_{a} (c) \log_{c} (a) + \log_{a} (c) \log_{c} (b)}{(1 + \log_{a} (b) + \log_{a} (c)) (1 + \log_{b} (c) + \log_{b} (a)) (1 + \log_{c} (a) + \log_{c} (b))}$