Pré-cálculo Exemplos

$\log (\sqrt[7]{\frac{s}{t}})$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ para reescrever $\sqrt[7]{\frac{s}{t}}$ como ${(\frac{s}{t})}^{\frac{1}{7}}$ .

$\log ({(\frac{s}{t})}^{\frac{1}{7}})$

Step 2

Expanda $\log ({(\frac{s}{t})}^{\frac{1}{7}})$ movendo $\frac{1}{7}$ para fora do logaritmo.

$\frac{1}{7} \log (\frac{s}{t})$

Step 3

Reescreva $\log (\frac{s}{t})$ como $\log (s) - \log (t)$ .

$\frac{1}{7} (\log (s) - \log (t))$

Step 4

Aplique a propriedade distributiva.

$\frac{1}{7} \log (s) + \frac{1}{7} (- \log (t))$

Step 5

Combine $\frac{1}{7}$ e $\log (s)$ .

$\frac{\log (s)}{7} + \frac{1}{7} (- \log (t))$

Step 6

Combine $\frac{1}{7}$ e $\log (t)$ .

$\frac{\log (s)}{7} - \frac{\log (t)}{7}$