Precalculus Examples

$\log_{5} (\frac{4 p}{5 k})$

Step 1

Rewrite $\log_{5} (\frac{4 p}{5 k})$ as $\log_{5} (4 p) - \log_{5} (5 k)$ .

$\log_{5} (4 p) - \log_{5} (5 k)$

Step 2

Rewrite $\log_{5} (4 p)$ as $\log_{5} (4) + \log_{5} (p)$ .

$\log_{5} (4) + \log_{5} (p) - \log_{5} (5 k)$

Step 3

Rewrite $\log_{5} (5 k)$ as $\log_{5} (5) + \log_{5} (k)$ .

$\log_{5} (4) + \log_{5} (p) - (\log_{5} (5) + \log_{5} (k))$

Step 4

Logarithm base $5$ of $5$ is $1$ .

$\log_{5} (4) + \log_{5} (p) - (1 + \log_{5} (k))$

Step 5

Simplify each term.

Tap for more steps...

Step 5.1

Rewrite $\log_{5} (4)$ as $\log_{5} (2^{2})$ .

$\log_{5} (2^{2}) + \log_{5} (p) - (1 + \log_{5} (k))$

Step 5.2

Expand $\log_{5} (2^{2})$ by moving $2$ outside the logarithm.

$2 \log_{5} (2) + \log_{5} (p) - (1 + \log_{5} (k))$

Step 5.3

Apply the distributive property.

$2 \log_{5} (2) + \log_{5} (p) - 1 \cdot 1 - \log_{5} (k)$

Step 5.4

Multiply $- 1$ by $1$ .

$2 \log_{5} (2) + \log_{5} (p) - 1 - \log_{5} (k)$