Precalculus Examples

$\frac{\ln (\sqrt{3 x - 5})}{7}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x - 5}$ as ${(3 x - 5)}^{\frac{1}{2}}$ .

$\frac{\ln ({(3 x - 5)}^{\frac{1}{2}})}{7}$

Step 2

Expand $\ln ({(3 x - 5)}^{\frac{1}{2}})$ by moving $\frac{1}{2}$ outside the logarithm.

$\frac{\frac{1}{2} \ln (3 x - 5)}{7}$

Step 3

Combine $\frac{1}{2}$ and $\ln (3 x - 5)$ .

$\frac{\frac{\ln (3 x - 5)}{2}}{7}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\frac{\ln (3 x - 5)}{2} \cdot \frac{1}{7}$

Step 5

Multiply $\frac{\ln (3 x - 5)}{2} \cdot \frac{1}{7}$ .

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Step 5.1

Multiply $\frac{\ln (3 x - 5)}{2}$ by $\frac{1}{7}$ .

$\frac{\ln (3 x - 5)}{2 \cdot 7}$

Step 5.2

Multiply $2$ by $7$ .

$\frac{\ln (3 x - 5)}{14}$