Write as a Single Logarithm 1/3 log base b of x-1- log base b of x+1

$\frac{1}{3} \log_{b} (x - 1) - \log_{b} (x + 1)$

Step 1

Simplify $\frac{1}{3} \log_{b} (x - 1)$ by moving $\frac{1}{3}$ inside the logarithm.

$\log_{b} ({(x - 1)}^{\frac{1}{3}}) - \log_{b} (x + 1)$

Step 2

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

$\log_{b} (\frac{{(x - 1)}^{\frac{1}{3}}}{x + 1})$