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

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

Step 1

Simplify each term.

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

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

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

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

Step 2

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log (x^{\frac{1}{3}} {(x - 3)}^{3})$