Write as a Single Logarithm 2( log base 3 of 20- log base 3 of 4)

$2 (\log_{3} (20) - \log_{3} (4))$

Step 1

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

$2 \log_{3} (\frac{20}{4})$

Step 2

Divide $20$ by $4$ .

$2 \log_{3} (5)$

Step 3

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

$\log_{3} (5^{2})$

Step 4

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

$\log_{3} (25)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log_{3} (25)$

Decimal Form:

$2.92994704 \dots$