Expand the Logarithmic Expression log of ( cube root of a)/b

$\log (\frac{\sqrt[3]{a}}{b})$

Step 1

Rewrite $\log (\frac{\sqrt[3]{a}}{b})$ as $\log (\sqrt[3]{a}) - \log (b)$ .

$\log (\sqrt[3]{a}) - \log (b)$

Step 2

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

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

Step 3

Expand $\log (a^{\frac{1}{3}})$ by moving $\frac{1}{3}$ outside the logarithm.

$\frac{1}{3} \log (a) - \log (b)$

Step 4

Combine $\frac{1}{3}$ and $\log (a)$ .

$\frac{\log (a)}{3} - \log (b)$