Precalculus Examples

$\log_{m} (a b^{2} \sqrt{c^{3}})$

Step 1

Rewrite $\log_{m} (a b^{2} \sqrt{c^{3}})$ as $\log_{m} (a b^{2}) + \log_{m} (\sqrt{c^{3}})$ .

$\log_{m} (a b^{2}) + \log_{m} (\sqrt{c^{3}})$

Step 2

Rewrite $\log_{m} (a b^{2})$ as $\log_{m} (a) + \log_{m} (b^{2})$ .

$\log_{m} (a) + \log_{m} (b^{2}) + \log_{m} (\sqrt{c^{3}})$

Step 3

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

$\log_{m} (a) + \log_{m} (b^{2}) + \log_{m} (c^{\frac{3}{2}})$

Step 4

Expand $\log_{m} (b^{2})$ by moving $2$ outside the logarithm.

$\log_{m} (a) + 2 \log_{m} (b) + \log_{m} (c^{\frac{3}{2}})$

Step 5

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

$\log_{m} (a) + 2 \log_{m} (b) + \frac{3}{2} \log_{m} (c)$

Step 6

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

$\log_{m} (a) + 2 \log_{m} (b) + \frac{3 \log_{m} (c)}{2}$