Evaluate ( log base 2 of x)^2

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

Remove parentheses.

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

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

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 $0$ .

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

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

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

Apply the product rule to $\frac{\log (x)}{\log (2)}$ .

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