Precalculus Examples

$\log (x^{3 \sqrt{y}}) \div z^{5}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y}$ as $y^{\frac{1}{2}}$ .

$\log (x^{3 y^{\frac{1}{2}}}) \div z^{5}$

Step 2

Expand $\log (x^{3 y^{\frac{1}{2}}})$ by moving $3 y^{\frac{1}{2}}$ outside the logarithm.

$3 y^{\frac{1}{2}} \log (x) \div z^{5}$

Step 3

Rewrite the division as a fraction.

$\frac{3 y^{\frac{1}{2}} \log (x)}{z^{5}}$