Evaluate log base 2 of 4^2*3^4

$\log_{2} (4^{2} \cdot 3^{4})$

Step 1

Raise $4$ to the power of $2$ .

$\log_{2} (16 \cdot 3^{4})$

Step 2

Raise $3$ to the power of $4$ .

$\log_{2} (16 \cdot 81)$

Step 3

Multiply $16$ by $81$ .

$\log_{2} (1296)$

Step 4

Rewrite $\log_{2} (1296)$ 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 $b = 10$ .

$\frac{\log (1296)}{\log (2)}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (1296)}{\log (2)}$

Decimal Form:

$10.33985000 \dots$