Question

o valor do logaritmo 1/32 na base 2√2 é??

Answer 1

$log_{2\sqrt2}(\frac{1}{32})=x\\ \\ (2\sqrt2)^x=\frac{1}{32}\\ \\ (2.2^{\frac{1}{2}})^x=\frac{1}{2^5}\\ \\ (2^{\frac{3}{2}})^x=2^{-5}\\ \\ 2^{\frac{3x}{2}}=2^{-5}\\ \\ \frac{3x}{2}=-5\\ \\ 3x=-10\\ \\ x=-\frac{10}{3}$