Precalculus Examples

$- 2 \log_{8} (5)$

Step 1

Simplify $- 2 \log_{8} (5)$ by moving $2$ inside the logarithm.

$- \log_{8} (5^{2})$

Step 2

Raise $5$ to the power of $2$ .

$- \log_{8} (25)$

Step 3

Rewrite $\log_{8} (25)$ 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 $b = 10$ .

$- \frac{\log (25)}{\log (8)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{\log (25)}{\log (8)}$

Decimal Form:

$- 1.54795206 \dots$