Finite Math Examples

$\ln (\sqrt{\frac{2 x - 1}{1 + x}})$

Step 1

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

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

Step 2

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

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

Step 3

Rewrite $\ln (\frac{2 x - 1}{1 + x})$ as $\ln (2 x - 1) - \ln (1 + x)$ .

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

Step 4

Apply the distributive property.

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

Step 5

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

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

Step 6

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

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

Step 7

Combine the numerators over the common denominator.

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