Question

Determine o valor de x nas equações abaixo:​

Answer 1

$\Large\boxed{\begin{array}{l}\tt a)~\sf 10^{x-1}=1000\\\sf 10^{x-1}=10^3\\\sf x-1=3\\\sf x=3+1\\\sf x=4\\\tt b)~\sf 5^{3-2x}=25\\\sf 5^{3-2x}=5^2\\\sf 3-2x=2\\\sf 2x=3-2\\\sf 2x=1\\\sf x=\dfrac{1}{2}\\\\\tt c)~\sf\bigg(\dfrac{3}{2}\bigg)^{3x}=\dfrac{16}{81}\\\sf\bigg(\dfrac{2}{3}\bigg)^{-3x}=\bigg(\dfrac{2}{3}\bigg)^4\\\sf -3x=4\cdot(-1)\\\sf 3x=-4\\\sf x=-\dfrac{4}{3}\end{array}}$

$\Large\boxed{\begin{array}{l}\tt d)~\sf 2^{4x+1}=\sqrt{0,5}\\\sf 2^{4x+1}=2^{-\frac{1}{2}}\\\sf 4x+1=-\dfrac{1}{2}\\\sf 8x+2=-1\\\sf 8x=-1-2\\\sf 8x=-3\\\sf x=-\dfrac{3}{8}\end{array}}$