Evaluate 2 log base 2 of 5

$2 \log_{2} (5)$

Step 1

Simplify $2 \log_{2} (5)$ by moving $2$ inside the logarithm.

$\log_{2} (5^{2})$

Step 2

Raise $5$ to the power of $2$ .

$\log_{2} (25)$

Step 3

Rewrite $\log_{2} (25)$ 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 $0$ .

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

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

$\frac{\log (25)}{\log (2)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (25)}{\log (2)}$

Decimal Form:

$4.64385618 \dots$