Trigonometry Examples

\frac{\ln (8)}{\frac{\ln (48)}{5}}

$\frac{\ln (8)}{\frac{\ln (48)}{5}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

\ln (8) \frac{5}{\ln (48)}

$\ln (8) \frac{5}{\ln (48)}$

Step 2

Rewrite

\ln (8)

$\ln (8)$ as

\ln (2^{3})

$\ln (2^{3})$ .

\ln (2^{3}) \frac{5}{\ln (48)}

$\ln (2^{3}) \frac{5}{\ln (48)}$

Step 3

Expand

\ln (2^{3})

$\ln (2^{3})$ by moving

3

$3$ outside the logarithm.

3 \ln (2) \frac{5}{\ln (48)}

$3 \ln (2) \frac{5}{\ln (48)}$

Step 4

Simplify the denominator.

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Step 4.1

Rewrite

\ln (48)

$\ln (48)$ as

\ln (2^{4} \cdot 3)

$\ln (2^{4} \cdot 3)$ .

3 \ln (2) \frac{5}{\ln (2^{4} \cdot 3)}

$3 \ln (2) \frac{5}{\ln (2^{4} \cdot 3)}$

Step 4.2

Rewrite

\ln (2^{4} \cdot 3)

$\ln (2^{4} \cdot 3)$ as

\ln (2^{4}) + \ln (3)

$\ln (2^{4}) + \ln (3)$ .

3 \ln (2) \frac{5}{\ln (2^{4}) + \ln (3)}

$3 \ln (2) \frac{5}{\ln (2^{4}) + \ln (3)}$

Step 4.3

Expand

\ln (2^{4})

$\ln (2^{4})$ by moving

4

$4$ outside the logarithm.

3 \ln (2) \frac{5}{4 \ln (2) + \ln (3)}

$3 \ln (2) \frac{5}{4 \ln (2) + \ln (3)}$

3 \ln (2) \frac{5}{4 \ln (2) + \ln (3)}

$3 \ln (2) \frac{5}{4 \ln (2) + \ln (3)}$

Step 5

Multiply

3 \ln (2) \frac{5}{4 \ln (2) + \ln (3)}

$3 \ln (2) \frac{5}{4 \ln (2) + \ln (3)}$ .

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Step 5.1

Combine

\frac{5}{4 \ln (2) + \ln (3)}

$\frac{5}{4 \ln (2) + \ln (3)}$ and

3

$3$ .

\frac{5 \cdot 3}{4 \ln (2) + \ln (3)} \ln (2)

$\frac{5 \cdot 3}{4 \ln (2) + \ln (3)} \ln (2)$

Step 5.2

Multiply

5

$5$ by

3

$3$ .

\frac{15}{4 \ln (2) + \ln (3)} \ln (2)

$\frac{15}{4 \ln (2) + \ln (3)} \ln (2)$

Step 5.3

Combine

\frac{15}{4 \ln (2) + \ln (3)}

$\frac{15}{4 \ln (2) + \ln (3)}$ and

\ln (2)

$\ln (2)$ .

\frac{15 \ln (2)}{4 \ln (2) + \ln (3)}

$\frac{15 \ln (2)}{4 \ln (2) + \ln (3)}$

\frac{15 \ln (2)}{4 \ln (2) + \ln (3)}

$\frac{15 \ln (2)}{4 \ln (2) + \ln (3)}$

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$