Question

O logaritmo de 7 na base b é -⅓. A base b desse logaritmo é igual a:

Answer 1

$\begin{array}{l}\log_{b} 7=-\frac{1}{3} \Leftrightarrow b^{-1/3} =7\\\\\Longrightarrow \frac{1}{\sqrt[3]{b}} =7\\\\\Longrightarrow \sqrt[3]{b} =\frac{1}{7}\\\\\Longrightarrow b=\frac{1^3}{7^{3}} =7^{-3}\end{array}$