Precalculus Examples

$(\frac{1}{3}) \log_{6} (4 x)$

Step 1

Simplify $(\frac{1}{3}) \log_{6} (4 x)$ by moving $\frac{1}{3}$ inside the logarithm.

$\log_{6} ({(4 x)}^{\frac{1}{3}})$

Step 2

Apply the product rule to $4 x$ .

$\log_{6} (4^{\frac{1}{3}} x^{\frac{1}{3}})$

Step 3

Rewrite $\log_{6} (4^{\frac{1}{3}} x^{\frac{1}{3}})$ 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 $b = 10$ .

$\frac{\log (4^{\frac{1}{3}} x^{\frac{1}{3}})}{\log (6)}$