Question

como resolvo log de raiz quadrada de 32 na base raiz de 8

Answer 1

$log_{\sqrt{8}}\ \sqrt{32} = x\\ \\ (\sqrt{8})^x = \sqrt{32}\\ \\ (2\sqrt{2})^x = 2^2\sqrt{2}\\ \\ (2^1~\cdot2^{\frac{1}{2}})^x = 2^2~\cdot2^{\frac{1}{2}}\\ \\ (2^{1+\frac{1}{2}})^x = 2^{2+\frac{1}{2}}\\ \\ (2^{\frac{3}{2}})^x = 2^{\frac{5}{2}}\\ \\ \frac{3x}{2} = \frac{5}{2}\\ \\ 3x = 5\\ \\ \large{\boxed{x=\frac{5}{3}}}$