Álgebra Exemplos

$\ln (\sqrt{x y})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescrever $\sqrt{x y}$ como ${(x y)}^{\frac{1}{2}}$ .

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

Step 2

Expanda $\ln ({(x y)}^{\frac{1}{2}})$ movendo $\frac{1}{2}$ para fora do logaritmo.

$\frac{1}{2} \ln (x y)$

Step 3

Reescreva $\ln (x y)$ como $\ln (x) + \ln (y)$ .

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

Step 4

Aplique a propriedade distributiva.

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

Step 5

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

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

Step 6

Combine $\frac{1}{2}$ e $\ln (y)$ .

$\frac{\ln (x)}{2} + \frac{\ln (y)}{2}$