Precalculus Examples

$\log_{b} (\sqrt{35})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{35}$ as $35^{\frac{1}{2}}$ .

$\log_{b} (35^{\frac{1}{2}})$

Step 2

Expand $\log_{b} (35^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\frac{1}{2} \log_{b} (35)$

Step 3

Rewrite $\log_{b} (35)$ as $\log_{b} (5 (7))$ .

$\frac{1}{2} \log_{b} (5 (7))$

Step 4

Rewrite $\log_{b} (5 (7))$ as $\log_{b} (5) + \log_{b} (7)$ .

$\frac{1}{2} (\log_{b} (5) + \log_{b} (7))$

Step 5

Apply the distributive property.

$\frac{1}{2} \log_{b} (5) + \frac{1}{2} \log_{b} (7)$

Step 6

Combine $\frac{1}{2}$ and $\log_{b} (5)$ .

$\frac{\log_{b} (5)}{2} + \frac{1}{2} \log_{b} (7)$

Step 7

Combine $\frac{1}{2}$ and $\log_{b} (7)$ .

$\frac{\log_{b} (5)}{2} + \frac{\log_{b} (7)}{2}$