Algebra Examples

$3 \log_{9} (x^{2})$

Step 1

Simplify $3 \log_{9} (x^{2})$ by moving $3$ inside the logarithm.

$\log_{9} ({(x^{2})}^{3})$

Step 2

Multiply the exponents in ${(x^{2})}^{3}$ .

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Step 2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\log_{9} (x^{2 \cdot 3})$

Step 2.2

Multiply $2$ by $3$ .

$\log_{9} (x^{6})$

Step 3

Rewrite $\log_{9} (x^{6})$ 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 $b = 10$ .

$\frac{\log (x^{6})}{\log (9)}$