Precalculus Examples

$\log (\frac{\sqrt{x}}{4})$

Step 1

Rewrite $\log (\frac{\sqrt{x}}{4})$ as $\log (\sqrt{x}) - \log (4)$ .

$\log (\sqrt{x}) - \log (4)$

Step 2

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

$\log (x^{\frac{1}{2}}) - \log (4)$

Step 3

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

$\frac{1}{2} \log (x) - \log (4)$

Step 4

Rewrite $\log (4)$ as $\log (2^{2})$ .

$\frac{1}{2} \log (x) - \log (2^{2})$

Step 5

Expand $\log (2^{2})$ by moving $2$ outside the logarithm.

$\frac{1}{2} \log (x) - (2 \log (2))$

Step 6

Multiply $2$ by $- 1$ .

$\frac{1}{2} \log (x) - 2 \log (2)$

Step 7

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

$\frac{\log (x)}{2} - 2 \log (2)$