Question

Me ajudem a responder a questão 4 pelo amor de DEUS!!!

Answer 1

a)

$3^{x-5}=27^{1-x}\\ \\ 3^{x-5}=(3^3)^{1-x}\\ \\ 3^{x-5}=3^{3-3x}\\ \\ x-5=3-3x\\ \\ x+3x=3+5\\ \\4x=8\\ \\ x=2$

b)

$10^{1-x}=\frac{1}{10}\\ \\ 10^{1-x}=10^{-1}\\ \\ 1-x=-1\\ \\ x=2$

c)

$9^{x-2}= \sqrt{27}\\ \\ (3^2)^{x-2}=3^{\frac{3}{2}}\\ \\ 2x-4=\frac{3}{2}\\ \\ 4x-8=3\\ \\ 4x=11\\ \\ x=\frac{11}{4}$

d)

$5^{2x-1}=1\\ \\ 2x-1=0\\ \\ x=\frac{1}{2}$

e)

$\left(\frac{2}{5}\right)^{x-1}=\frac{125}{8}\\ \\ \left(\frac{2}{5}\right)^{x-1}=(\frac{5}{2})^3\\ \\ \left(\frac{2}{5}\right)^{x-1}=(\frac{2}{5})^{-3}\\ \\ x-1=-3\\ \\ x=-2$