Precalculus Examples

$\log (b) \cdot (4 \sqrt{\frac{x^{7} (y^{2})}{z^{4}}})$

Step 1

Rewrite using the commutative property of multiplication.

$4 \log (b) \sqrt{\frac{x^{7} y^{2}}{z^{4}}}$

Step 2

Simplify $4 \log (b)$ by moving $4$ inside the logarithm.

$\log (b^{4}) \sqrt{\frac{x^{7} y^{2}}{z^{4}}}$

Step 3

Rewrite $\frac{x^{7} y^{2}}{z^{4}}$ as ${(\frac{x^{3} y}{z^{2}})}^{2} x$ .

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Step 3.1

Factor the perfect power ${(x^{3} y)}^{2}$ out of $x^{7} y^{2}$ .

$\log (b^{4}) \sqrt{\frac{{(x^{3} y)}^{2} x}{z^{4}}}$

Step 3.2

Factor the perfect power ${(z^{2})}^{2}$ out of $z^{4}$ .

$\log (b^{4}) \sqrt{\frac{{(x^{3} y)}^{2} x}{{(z^{2})}^{2} \cdot 1}}$

Step 3.3

Rearrange the fraction $\frac{{(x^{3} y)}^{2} x}{{(z^{2})}^{2} \cdot 1}$ .

$\log (b^{4}) \sqrt{{(\frac{x^{3} y}{z^{2}})}^{2} x}$

Step 4

Pull terms out from under the radical.

$\log (b^{4}) (\frac{x^{3} y}{z^{2}} \sqrt{x})$

Step 5

Combine $\frac{x^{3} y}{z^{2}}$ and $\sqrt{x}$ .

$\log (b^{4}) \frac{x^{3} y \sqrt{x}}{z^{2}}$

Step 6

Combine $\log (b^{4})$ and $\frac{x^{3} y \sqrt{x}}{z^{2}}$ .

$\frac{\log (b^{4}) (x^{3} y \sqrt{x})}{z^{2}}$

Step 7

Reorder factors in $\frac{\log (b^{4}) x^{3} y \sqrt{x}}{z^{2}}$ .

$\frac{x^{3} y \log (b^{4}) \sqrt{x}}{z^{2}}$