Simplify/Condense 4 log of 3-4 log of 8

$4 \log (3) - 4 \log (8)$

Step 1

Simplify each term.

Simplify $4 \log (3)$ by moving $4$ inside the logarithm.

$\log (3^{4}) - 4 \log (8)$

Raise $3$ to the power of $4$ .

$\log (81) - 4 \log (8)$

Simplify $- 4 \log (8)$ by moving $4$ inside the logarithm.

$\log (81) - \log (8^{4})$

Raise $8$ to the power of $4$ .

$\log (81) - \log (4096)$

Step 2

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

$\log (\frac{81}{4096})$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\log (\frac{81}{4096})$

Decimal Form:

$- 1.70387492 \dots$