Precalculus Examples

$\log_{2} ({(8)}^{33})$

Step 1

Remove parentheses.

$\log_{2} (8^{33})$

Step 2

Rewrite $\log_{2} (8^{33})$ using the change of base formula.

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Step 2.1

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 2.2

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

$\frac{\log (8^{33})}{\log (2)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (8^{33})}{\log (2)}$

Decimal Form:

$99$