Precalculus Examples

$\frac{\ln (a^{3} b^{- 2})}{\ln ({(b c)}^{4})}$

Step 1

Rewrite $\ln (a^{3} b^{- 2})$ as $\ln (a^{3}) + \ln (b^{- 2})$ .

$\frac{\ln (a^{3}) + \ln (b^{- 2})}{\ln ({(b c)}^{4})}$

Step 2

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

$\frac{3 \ln (a) + \ln (b^{- 2})}{\ln ({(b c)}^{4})}$

Step 3

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

$\frac{3 \ln (a) - 2 \ln (b)}{\ln ({(b c)}^{4})}$

Step 4

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

$\frac{3 \ln (a) - 2 \ln (b)}{4 \ln (b c)}$

Step 5

Rewrite $\ln (b c)$ as $\ln (b) + \ln (c)$ .

$\frac{3 \ln (a) - 2 \ln (b)}{4 (\ln (b) + \ln (c))}$