Algebra Examples

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

Step 1

Remove parentheses.

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

Step 2

Rewrite $\log_{9} (x)$ 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 $0$ .

$3 {\log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}}^{2}$

Step 2.2

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

$3 {(\frac{\log (x)}{\log (9)})}^{2}$

Step 3

Apply the product rule to $\frac{\log (x)}{\log (9)}$ .

$3 \frac{\log^{2} (x)}{\log^{2} (9)}$

Step 4

Combine $3$ and $\frac{\log^{2} (x)}{\log^{2} (9)}$ .

$\frac{3 \log^{2} (x)}{\log^{2} (9)}$