Question

resolva as exponencial

$a) {243}^{x} = \sqrt[4]{3}$
$b) \frac{1}{2} {}^{x} = 1024$
$c)( {25})^{2x} = 0.2$

Answer 1

$a)\\243^x=3^{\frac{1}{4}}\\\\(3^5)^x=3^{\frac{1}{4}}\\\\3^{5.x}=3^{\frac{1}{4}}\\\\5x=\frac{1}{4}\\\\x=\frac{5}{4}=1,25$

$b)\\(2^{-1})^x=2^{10}\\\\2^{-1x}=2^{10}\\\\-x=10\\\\x=-10$

$c)\\(5^2)^{2x}=\frac{1}{5}\\\\5^{2.2x}=5^{-1}\\\\4x=-1\\\\x=-\frac{1}{4}=-0,25$