Write as a Single Logarithm log base 3 of 6+2* log base 3 of x+1/2 log base 3 of 9

$\log_{3} (6) + 2 \cdot \log_{3} (x) + \frac{1}{2} \log_{3} (9)$

Simplify each term.

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

$\log_{3} (6) + \log_{3} (x^{2}) + \frac{1}{2} \cdot \log_{3} (9)$

Logarithm base $3$ of $9$ is $2$ .

$\log_{3} (6) + \log_{3} (x^{2}) + \frac{1}{2} \cdot 2$

Cancel the common factor of $2$ .

Cancel the common factor.

$\log_{3} (6) + \log_{3} (x^{2}) + \frac{1}{2} \cdot 2$

Rewrite the expression.

$\log_{3} (6) + \log_{3} (x^{2}) + 1$

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

$\log_{3} (6 x^{2}) + 1$