Precalculus Examples

$\log ({(4)}^{\frac{x y^{3}}{z^{6}}})$

Step 1

Expand $\log ({(4)}^{\frac{x y^{3}}{z^{6}}})$ by moving $\frac{x y^{3}}{z^{6}}$ outside the logarithm.

$\frac{x y^{3}}{z^{6}} \log (4)$

Step 2

Combine $\frac{x y^{3}}{z^{6}}$ and $\log (4)$ .

$\frac{x y^{3} \log (4)}{z^{6}}$

Step 3

Simplify the numerator.

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Step 3.1

Rewrite $\log (4)$ as $\log (2^{2})$ .

$\frac{x y^{3} \log (2^{2})}{z^{6}}$

Step 3.2

Expand $\log (2^{2})$ by moving $2$ outside the logarithm.

$\frac{x y^{3} \cdot 2 \log (2)}{z^{6}}$

Step 4

Move $2$ to the left of $x y^{3}$ .

$\frac{2 x y^{3} \log (2)}{z^{6}}$