Question

Resolva as equações exponenciais:
A) (0,2) (elevado na x-2) = 1
B) (1/3) (elevado na x+1) = (9/4) (elevado na 1+2x)
C) (1/3) (elevado na -4+x) = 9 (elevado na x+3)
D) 5 (elevado na 2-x) = 1/125 

Answer 1

a)
$0,2^{x-2}= 1 \\ (\frac{1}{5})^{x-2}= 5^0 \\ (5^{-1})^{x-2}= 5^0 \\ 5^{-x+2}= 5^0 \\ -x+2=0 \\ -x= -2 \\ x= 2$

b)
$(\frac{3}{2})^{x+1}= (\frac{9}{4})^{1+2x} \\ \\ (\frac{3}{2})^{x+1}= ((\frac{3}{2})^{2})^{1+2x} \\ \\ (\frac{3}{2})^{x+1}= (\frac{3}{2})^{2+4x} \\ x+1=2+4x\\ x-4x= 2-1\\ -3x=1 \\ x= - {\frac{1}{3}$

c)
$\frac{1}{3} ^{-4+x} = 9^{x+3} \\ (3^{-1})^{-4x+x}= (3^2)^{x+3} \\ 3^{4x-x}= 3^{2x+6}\\ 4x-x= 2x+6 \\ 4x-x-2x=6 \\x=6$

d)
$5^{2-x}= \frac{1}{125} \\ 5^{2-x}= 5^{-3} \\ 2-x= -3 \\ -x= -3-2 \\ -x=-5 \\ x=5$