Question

Função exponencial, ajuda!!

a) (raiz quadrada de 0,1)^x = raiz cubica de 10.

b) 3/5^ -x +2 = raiz cubica de 5/3

c) 5 raiz quarta de 2^x = 160

Desde já, agradeço!

Answer 1

$a)( \sqrt{ 0,1})^{x}= \sqrt[3]{10} = (\sqrt{ \frac{1}{10} } )^{x}=( \sqrt{10^{-1}} )^{x}=(10^{ \frac{-1}{2} })^{x}=10^-{ \frac{x}{2} }=10^ \frac{1}{3} =>- \frac{x}{2} = \frac{1}{3} =>x=- \frac{2}{3}$
$b) (\frac{3}{5} )^{-x+2}= \sqrt[3]{ \frac{5}{3} } = \frac{5}{3} ^{ \frac{1}{3} }= \frac{3}{5} ^{- \frac{1}{3} }=> -x+2=-\frac{1}{3} => x=7/3$
$d)5 \sqrt[4]{2^{x}} =160=>2 ^{\frac{x}{4} }= \frac{160}{5} =32=2^{5}=> \frac{x}{4} =5=>x=20$