Trigonometry Examples

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

Step 1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2

Rewrite $\ln (8)$ as $\ln (2^{3})$ .

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

Step 3

Expand $\ln (2^{3})$ by moving $3$ outside the logarithm.

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

Step 4

Simplify the denominator.

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Step 4.1

Rewrite $\ln (48)$ as $\ln (2^{4} \cdot 3)$ .

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

Step 4.2

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

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

Step 4.3

Expand $\ln (2^{4})$ by moving $4$ outside the logarithm.

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Multiply $5$ by $3$ .

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

Step 5.3

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

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