Precalculus Examples

$\log (\sqrt{z x^{9} y^{4}})$

Step 1

Rewrite $z x^{9} y^{4}$ as ${(x^{4} y^{2})}^{2} (z x)$ .

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Step 1.1

Factor out $x^{8}$ .

$\log (\sqrt{z (x^{8} x) y^{4}})$

Step 1.2

Rewrite $x^{8}$ as ${(x^{4})}^{2}$ .

$\log (\sqrt{z ({(x^{4})}^{2} x) y^{4}})$

Step 1.3

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

$\log (\sqrt{z ({(x^{4})}^{2} x) {(y^{2})}^{2}})$

Step 1.4

Move $x$ .

$\log (\sqrt{z ({(x^{4})}^{2}) {(y^{2})}^{2} x})$

Step 1.5

Move $z$ .

$\log (\sqrt{({(x^{4})}^{2}) {(y^{2})}^{2} z x})$

Step 1.6

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

$\log (\sqrt{{(x^{4} y^{2})}^{2} z x})$

Step 1.7

Add parentheses.

$\log (\sqrt{{(x^{4} y^{2})}^{2} (z x)})$

Step 2

Pull terms out from under the radical.

$\log (x^{4} y^{2} \sqrt{z x})$