Precalculus Examples

$\log_{2} (x - \log_{2} (y \sqrt{z^{3}}))$

Step 1

Rewrite $\log_{2} (y \sqrt{z^{3}})$ as $\log_{2} (y) + \log_{2} (\sqrt{z^{3}})$ .

$\log_{2} (x - (\log_{2} (y) + \log_{2} (\sqrt{z^{3}})))$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{z^{3}}$ as $z^{\frac{3}{2}}$ .

$\log_{2} (x - (\log_{2} (y) + \log_{2} (z^{\frac{3}{2}})))$

Step 3

Expand $\log_{2} (z^{\frac{3}{2}})$ by moving $\frac{3}{2}$ outside the logarithm.

$\log_{2} (x - (\log_{2} (y) + \frac{3}{2} \log_{2} (z)))$

Step 4

Combine $\frac{3}{2}$ and $\log_{2} (z)$ .

$\log_{2} (x - (\log_{2} (y) + \frac{3 \log_{2} (z)}{2}))$

Step 5

Apply the distributive property.

$\log_{2} (x - \log_{2} (y) - \frac{3 \log_{2} (z)}{2})$