Precalculus Examples

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

Step 1

Simplify the numerator.

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Step 1.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{\ln (\frac{1}{a^{2}} b^{4})}{\ln ({(b c)}^{4})}$

Step 1.2

Combine $\frac{1}{a^{2}}$ and $b^{4}$ .

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

Step 2

Apply the product rule to $b c$ .

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