Expand log of square root of b^6c

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

Rewrite $\sqrt{b^{6} c}$ as ${(b^{6} c)}^{\frac{1}{2}}$ .

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

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

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

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

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

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

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

Apply the distributive property.

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

Cancel the common factor of $2$ .

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Expand log of square root of b^6c