Question

Mostre que : log√a c = 2b sabendo que a^b=c
√a é a base do log

Answer 1

Olá, Bruno.

$c=a^b\Rightarrow \\\\\log_{\sqrt a}\,c=\log_{\sqrt a}\,a^b\Rightarrow\\\\ \log_{\sqrt a}\,c=b\cdot\log_{\sqrt a}\,a\Rightarrow\\\\ \log_{\sqrt a}\,c=b\cdot\log_{a^\frac12}\,a\Rightarrow\\\\ \log_{\sqrt a}\,c=b\cdot\frac{1}{\log_{a}\,a^\frac12}\Rightarrow\\\\ \log_{\sqrt a}\,c=b\cdot\frac{1}{\frac12}\Rightarrow\\\\ \log_{\sqrt a}\,c=b\cdot2\Rightarrow\\\\ \boxed{\log_{\sqrt a}c = 2b}$