Evaluate log base 6 of 4+2 log base 6 of 3

$\log_{6} (4) + 2 \log_{6} (3)$

Simplify each term.

Simplify $2 \log_{6} (3)$ by moving $2$ inside the logarithm.

$\log_{6} (4) + \log_{6} (3^{2})$

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

$\log_{6} (4) + \log_{6} (9)$

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

$\log_{6} (4 \cdot 9)$

Multiply $4$ by $9$ .

$\log_{6} (36)$

Logarithm base $6$ of $36$ is $2$ .

$2$