Precalculus Examples

$2 \log_{2} (3)$

Step 1

Simplify $2 \log_{2} (3)$ by moving $2$ inside the logarithm.

$\log_{2} (3^{2})$

Step 2

Raise $3$ to the power of $2$ .

$\log_{2} (9)$

Step 3

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

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$3.16992500 \dots$