Solve for x 1/2* log base 3 of x=2 log base 3 of 2

$\frac{1}{2} \cdot \log_{3} (x) = 2 \log_{3} (2)$

Step 1

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot \log_{3} (x)) = 2 (2 \log_{3} (2))$

Step 2

Simplify both sides of the equation.

Simplify the left side.

Simplify $2 (\frac{1}{2} \cdot \log_{3} (x))$ .

Combine $\frac{1}{2}$ and $\log_{3} (x)$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Multiply $2$ by $2$ .

$\log_{3} (x) = 4 \log_{3} (2)$

Step 3

Simplify $4 \log_{3} (2)$ by moving $4$ inside the logarithm.

$\log_{3} (x) = \log_{3} (2^{4})$

Step 4

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$x = 2^{4}$

Step 5

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

$x = 16$