Expand the Logarithmic Expression log of square root of b^3c

$\log (\sqrt{b^{3} c})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{b^{3} c}$ as ${(b^{3} c)}^{\frac{1}{2}}$ .

$\log ({(b^{3} c)}^{\frac{1}{2}})$

Expand $\log ({(b^{3} c)}^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\frac{1}{2} \log (b^{3} c)$

Rewrite $\log (b^{3} c)$ as $\log (b^{3}) + \log (c)$ .

$\frac{1}{2} (\log (b^{3}) + \log (c))$

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

$\frac{1}{2} (3 \log (b) + \log (c))$

Apply the distributive property.

$\frac{1}{2} (3 \log (b)) + \frac{1}{2} \log (c)$

Multiply $\frac{1}{2} (3 \log (b))$ .

Combine $3$ and $\frac{1}{2}$ .

$\frac{3}{2} \log (b) + \frac{1}{2} \log (c)$

Combine $\frac{3}{2}$ and $\log (b)$ .

$\frac{3 \log (b)}{2} + \frac{1}{2} \log (c)$

Combine $\frac{1}{2}$ and $\log (c)$ .

$\frac{3 \log (b)}{2} + \frac{\log (c)}{2}$