Question

ALGUEM SABE FAZER A LETRA I E LETRA M

Answer 1

Explicação passo-a-passo:

i) $\left(\dfrac{1}{4}\right)^{2x-3}=4$

Note que $\dfrac{1}{4}=\dfrac{1}{2^2}=2^{-2}$ e $4=2^{2}$

$(2^{-2})^{2x-3}=2^2$

$2^{-4x+6}=2^2$

$-4x+6=2$

$-4x=-4$

$\boxed{x=1}$

m) $\left(\dfrac{3}{2}\right)^{x+1}=\left(\dfrac{9}{4}\right)^{1+2x}$

Veja que $\dfrac{9}{4}=\dfrac{3^2}{2^2}=\left(\dfrac{3}{2}\right)^2$

$\left(\dfrac{3}{2}\right)^{x+1}=\left[\left(\dfrac{3}{2}\right)^2\right]^{1+2x}$

$\left(\dfrac{3}{2}\right)^{x+1}=\left(\dfrac{3}{2}\right)^{2+4x}$

$x+1=2+4x$

$x-4x=2-1$

$-3x=1$

$\boxed{x=-\dfrac{1}{3}}$