Precalculus Examples

$\frac{\log_{8} (x)}{\log_{8} (2)}$

Step 1

Logarithm base $8$ of $2$ is $\frac{1}{3}$ .

$\frac{\log_{8} (x)}{\frac{1}{3}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\log_{8} (x) \cdot 3$

Step 3

Multiply $\log_{8} (x) \cdot 3$ .

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Step 3.1

Reorder $\log_{8} (x)$ and $3$ .

$3 \cdot \log_{8} (x)$

Step 3.2

Simplify $3 \cdot \log_{8} (x)$ by moving $3$ inside the logarithm.

$\log_{8} (x^{3})$

Step 4

Rewrite $\log_{8} (x^{3})$ 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 $b = 10$ .

$\frac{\log (x^{3})}{\log (8)}$