Write as a Single Logarithm 2* log base 3 of 8-4* log base 3 of 2

$2 \cdot \log_{3} (8) - 4 \cdot \log_{3} (2)$

Step 1

Simplify each term.

Simplify $2 \log_{3} (8)$ by moving $2$ inside the logarithm.

$\log_{3} (8^{2}) - 4 \cdot \log_{3} (2)$

Raise $8$ to the power of $2$ .

$\log_{3} (64) - 4 \cdot \log_{3} (2)$

Simplify $- 4 \log_{3} (2)$ by moving $4$ inside the logarithm.

$\log_{3} (64) - \log_{3} (2^{4})$

Raise $2$ to the power of $4$ .

$\log_{3} (64) - \log_{3} (16)$

Step 2

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

$\log_{3} (\frac{64}{16})$

Step 3

Divide $64$ by $16$ .

$\log_{3} (4)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log_{3} (4)$

Decimal Form:

$1.26185950 \dots$