Precalculus Examples

$\log_{15} (\frac{11 (\sqrt{x})}{y})$

Step 1

Rewrite $\log_{15} (\frac{11 (\sqrt{x})}{y})$ as $\log_{15} (11 (\sqrt{x})) - \log_{15} (y)$ .

$\log_{15} (11 (\sqrt{x})) - \log_{15} (y)$

Step 2

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

$\log_{15} (11 x^{\frac{1}{2}}) - \log_{15} (y)$

Step 3

Rewrite $\log_{15} (11 x^{\frac{1}{2}})$ as $\log_{15} (11) + \log_{15} (x^{\frac{1}{2}})$ .

$\log_{15} (11) + \log_{15} (x^{\frac{1}{2}}) - \log_{15} (y)$

Step 4

Expand $\log_{15} (x^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\log_{15} (11) + \frac{1}{2} \log_{15} (x) - \log_{15} (y)$

Step 5

Combine $\frac{1}{2}$ and $\log_{15} (x)$ .

$\log_{15} (11) + \frac{\log_{15} (x)}{2} - \log_{15} (y)$