Question

calcule: log raiz de 32 na base raiz de 8

Answer 1

$log_{ \sqrt{8} } \sqrt{32} = x \\ \\ ( \sqrt{8} )^{x}= \sqrt{32} \\ \\ (8^{ \frac{1}{2} })^{x}= \sqrt{2^{5}} \\ \\ ((2^{3})^{ \frac{1}{2} })^{x}= 2^{ \frac{5}{2} } \\ \\ 2^{ \frac{3}{2}x }= 2^{ \frac{5}{2} } \\ \\ \frac{3}{2} x = \frac{5}{2} \\ \\ 3x=5 \\ \\ x = \frac{5}{3}$

Espero ter ajudado.