Algebra Examples

$\ln (\frac{1}{\sqrt{7 x - 3}})$

Step 1

Rewrite $\ln (\frac{1}{\sqrt{7 x - 3}})$ as $\ln (1) - \ln (\sqrt{7 x - 3})$ .

$\ln (1) - \ln (\sqrt{7 x - 3})$

Step 2

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7 x - 3}$ as ${(7 x - 3)}^{\frac{1}{2}}$ .

$\ln (1) - \ln ({(7 x - 3)}^{\frac{1}{2}})$

Step 3

Expand $\ln ({(7 x - 3)}^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\ln (1) - (\frac{1}{2} \ln (7 x - 3))$

Step 4

The natural logarithm of $1$ is $0$ .

$0 - (\frac{1}{2} \ln (7 x - 3))$

Step 5

Combine $\frac{1}{2}$ and $\ln (7 x - 3)$ .

$0 - \frac{\ln (7 x - 3)}{2}$

Step 6

Subtract $\frac{\ln (7 x - 3)}{2}$ from $0$ .

$- \frac{\ln (7 x - 3)}{2}$