Simplify log base 2 of 36-2 log base 2 of 3

$\log_{2} (36) - 2 \log_{2} (3)$

Step 1

Simplify each term.

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

$\log_{2} (36) - \log_{2} (3^{2})$

Raise $3$ to the power of $2$ .

$\log_{2} (36) - \log_{2} (9)$

Step 2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log_{2} (\frac{36}{9})$

Step 3

Logarithm base $2$ of $\frac{36}{9}$ is $2$ .

$2$