Write as a Single Logarithm log base 3 of 4x^2y+ log base 3 of 5x^3y^2

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

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

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

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $3$ and $2$ .

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

Multiply $y$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

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

Multiply $y^{2}$ by $y$ .

Raise $y$ to the power of $1$ .

$\log_{3} (4 x^{5} (y^{2} y^{1}) \cdot 5)$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\log_{3} (4 x^{5} y^{2 + 1} \cdot 5)$

Add $2$ and $1$ .

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

Multiply $5$ by $4$ .

$\log_{3} (20 x^{5} y^{3})$