Precalculus Examples

$\log (5) \sqrt{\frac{x^{4}}{9 b^{6}}}$

Step 1

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

$\log (5) \sqrt{\frac{{(x^{2})}^{2}}{9 b^{6}}}$

Step 2

Rewrite $9 b^{6}$ as ${(3 b^{3})}^{2}$ .

$\log (5) \sqrt{\frac{{(x^{2})}^{2}}{{(3 b^{3})}^{2}}}$

Step 3

Rewrite $\frac{{(x^{2})}^{2}}{{(3 b^{3})}^{2}}$ as ${(\frac{x^{2}}{3 b^{3}})}^{2}$ .

$\log (5) \sqrt{{(\frac{x^{2}}{3 b^{3}})}^{2}}$

Step 4

Pull terms out from under the radical, assuming positive real numbers.

$\log (5) \frac{x^{2}}{3 b^{3}}$

Step 5

Combine $\log (5)$ and $\frac{x^{2}}{3 b^{3}}$ .

$\frac{\log (5) x^{2}}{3 b^{3}}$

Step 6

Reorder factors in $\frac{\log (5) x^{2}}{3 b^{3}}$ .

$\frac{x^{2} \log (5)}{3 b^{3}}$