Expand the Logarithmic Expression log of square root of c^6d

$\log (\sqrt{c^{6} d})$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{c^{6} d}$ as ${(c^{6} d)}^{\frac{1}{2}}$ .

$\log ({(c^{6} d)}^{\frac{1}{2}})$

Expand $\log ({(c^{6} d)}^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\frac{1}{2} \log (c^{6} d)$

Rewrite $\log (c^{6} d)$ as $\log (c^{6}) + \log (d)$ .

$\frac{1}{2} (\log (c^{6}) + \log (d))$

Expand $\log (c^{6})$ by moving $6$ outside the logarithm.

$\frac{1}{2} (6 \log (c) + \log (d))$

Apply the distributive property.

$\frac{1}{2} (6 \log (c)) + \frac{1}{2} \log (d)$

Cancel the common factor of $2$ .

Factor $2$ out of $6 \log (c)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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