Expand the Logarithmic Expression log base 2 of cube root of 4x-5

$\log_{2} (\sqrt[3]{4 x - 5})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{4 x - 5}$ as ${(4 x - 5)}^{\frac{1}{3}}$ .

$\log_{2} ({(4 x - 5)}^{\frac{1}{3}})$

Step 2

Expand $\log_{2} ({(4 x - 5)}^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$\frac{1}{3} \log_{2} (4 x - 5)$

Step 3

Combine $\frac{1}{3}$ and $\log_{2} (4 x - 5)$ .

$\frac{\log_{2} (4 x - 5)}{3}$