Question

1) Resolva usando as propriedades da potência

a) 2 ². 4⁵ = 8ˣ

b) 81/x = 9³

Answer 1

a) $2^2\cdot 4^5=8^x$

$2^2\cdot(2^2)^5=(2^3)^x$

$2^2\cdot2^{10}=2^{3x}$

$2^{12}=2^{3x}$

$12=3x$

$3x=12$

$x=\frac{12}{3}$

$x=4$

b) $\frac{81}{x}=9^3$

$81=x\cdot9^3$

$x\cdot9^3=81$

$x\cdot9^3=9^2$

$x=\frac{9^2}{9^3}$

$x=9^{-1}$

$x=\frac{1}{9}$