Precalculus Examples

$\log_{\sqrt{7}} (49)$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7}$ as $7^{\frac{1}{2}}$ .

$\log_{7^{\frac{1}{2}}} (49)$

Step 2

Rewrite $\log_{7^{\frac{1}{2}}} (49)$ as $\log_{7^{\frac{1}{2}}} (7^{2})$ .

$\log_{7^{\frac{1}{2}}} (7^{2})$

Step 3

Expand $\log_{7^{\frac{1}{2}}} (7^{2})$ by moving $2$ outside the logarithm.

$2 \log_{7^{\frac{1}{2}}} (7)$