Evaluate log base 3 of 2+2 log base 3 of x

$\log_{3} (2) + 2 \log_{3} (x)$

Step 1

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

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

Step 2

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

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

Step 3

Rewrite $\log_{3} (2 x^{2})$ 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 $b = 10$ .

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