Question

resolva a equação exponencial usando artificio. 10.2^x-³=40

Answer 1

$10. (2^{x} ) ^{-3} =40$

                     $artificio: 2^{x} =y$

$10. y^{-3} =40$

$10. \frac{1}{y ^{3} } =40$

$\frac{10}{ y^{3} } =40$

$40y^{3} =10$

$y^{2} = \frac{10}{40}$

$y^{3} = \frac{1}{4}$

$y= \sqrt[3]{ \frac{1}{4} }$

$2^{x} = \sqrt[3]{ \frac{1}{4} } = 2^{x} =(4 ^{-1} ) ^{ (\frac{1}{3}) }$

$2^{x} =(2 ^{2}) ^{-1} ) ^{ (\frac{1}{3}) }$

$2^{x} =2 ^{\frac{-2}{3} }$

$x= \frac{-2}{3}$ $resposta$