Simplify/Condense log base 3 of 4+2 log base 3 of x- log base 3 of 5

$\log_{3} (4) + 2 \log_{3} (x) - \log_{3} (5)$

Step 1

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

$2 \log_{3} (x) + \log_{3} (\frac{4}{5})$

Step 2

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

$\log_{3} (x^{2}) + \log_{3} (\frac{4}{5})$

Step 3

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

$\log_{3} (x^{2} \frac{4}{5})$

Step 4

Combine $x^{2}$ and $\frac{4}{5}$ .

$\log_{3} (\frac{x^{2} \cdot 4}{5})$

Step 5

Move $4$ to the left of $x^{2}$ .

$\log_{3} (\frac{4 x^{2}}{5})$