Precalculus Examples

$\log_{6} ({(\frac{x}{y^{7}})}^{4})$

Step 1

Apply the product rule to $\frac{x}{y^{7}}$ .

$\log_{6} (\frac{x^{4}}{{(y^{7})}^{4}})$

Step 2

Multiply the exponents in ${(y^{7})}^{4}$ .

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Step 2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\log_{6} (\frac{x^{4}}{y^{7 \cdot 4}})$

Step 2.2

Multiply $7$ by $4$ .

$\log_{6} (\frac{x^{4}}{y^{28}})$

Step 3

Rewrite $\log_{6} (\frac{x^{4}}{y^{28}})$ using the change of base formula.

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Step 3.1

The change of base rule can be used if $a$ and $b$ are greater than $0$ and not equal to $1$ , and $x$ is greater than $0$ .

$\log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}$

Step 3.2

Substitute in values for the variables in the change of base formula, using $b = 10$ .

$\frac{\log (\frac{x^{4}}{y^{28}})}{\log (6)}$