Precalculus Examples

$\log_{2} (9) \cdot 2^{9}$

Step 1

Raise $2$ to the power of $9$ .

$\log_{2} (9) \cdot 512$

Step 2

Multiply $\log_{2} (9) \cdot 512$ .

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Step 2.1

Reorder $\log_{2} (9)$ and $512$ .

$512 \cdot \log_{2} (9)$

Step 2.2

Simplify $512 \cdot \log_{2} (9)$ by moving $512$ inside the logarithm.

$\log_{2} (9^{512})$

Step 3

Rewrite $\log_{2} (9^{512})$ 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 $b = 10$ .

$\frac{\log (9^{512})}{\log (2)}$