Trigonometry Examples

$\frac{\ln (13)}{\ln (25) - \ln (20)}$

Step 1

Rewrite $\ln (25)$ as $\ln (5^{2})$ .

$\frac{\ln (13)}{\ln (5^{2}) - \ln (20)}$

Step 2

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

$\frac{\ln (13)}{2 \ln (5) - \ln (20)}$

Step 3

Rewrite $\ln (20)$ as $\ln (2^{2} \cdot 5)$ .

$\frac{\ln (13)}{2 \ln (5) - \ln (2^{2} \cdot 5)}$

Step 4

Rewrite $\ln (2^{2} \cdot 5)$ as $\ln (2^{2}) + \ln (5)$ .

$\frac{\ln (13)}{2 \ln (5) - (\ln (2^{2}) + \ln (5))}$

Step 5

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

$\frac{\ln (13)}{2 \ln (5) - (2 \ln (2) + \ln (5))}$

Step 6

Apply the distributive property.

$\frac{\ln (13)}{2 \ln (5) - (2 \ln (2)) - \ln (5)}$

Step 7

Multiply $2$ by $- 1$ .

$\frac{\ln (13)}{2 \ln (5) - 2 \ln (2) - \ln (5)}$

Step 8

Subtract $\ln (5)$ from $2 \ln (5)$ .

$\frac{\ln (13)}{\ln (5) - 2 \ln (2)}$