Precalculus Examples

$- 4 \log_{6} (2 x)$

Step 1

Simplify $- 4 \log_{6} (2 x)$ by moving $4$ inside the logarithm.

$- \log_{6} ({(2 x)}^{4})$

Step 2

Apply the product rule to $2 x$ .

$- \log_{6} (2^{4} x^{4})$

Step 3

Raise $2$ to the power of $4$ .

$- \log_{6} (16 x^{4})$

Step 4

Rewrite $\log_{6} (16 x^{4})$ using the change of base formula.

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Step 4.1

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 4.2

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

$- \frac{\log (16 x^{4})}{\log (6)}$