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

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

Step 1

Simplify each term.

Simplify $2 \log_{3} (5 y)$ by moving $2$ inside the logarithm.

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

Apply the product rule to $5 y$ .

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

Raise $5$ to the power of $2$ .

$\log_{3} (4 x) + \log_{3} (25 y^{2})$

Step 2

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

$\log_{3} (4 x (25 y^{2}))$

Step 3

Rewrite using the commutative property of multiplication.

$\log_{3} (4 \cdot 25 x y^{2})$

Step 4

Multiply $4$ by $25$ .

$\log_{3} (100 x y^{2})$