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

$3 \log_{b} (2) - \log_{b} (8)$

Step 1

Simplify each term.

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

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

Raise $2$ to the power of $3$ .

$\log_{b} (8) - \log_{b} (8)$

Step 2

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

$\log_{b} (\frac{8}{8})$

Step 3

Divide $8$ by $8$ .

$\log_{b} (1)$

Step 4

Logarithm base $b$ of $1$ is $0$ .

$0$