Question

Determine o conjunto verdade das equações exponenciais:

a) 8^x = 32
b) 9^x = 1/3
c) (2/3) = 8/27
d) 2^x+4 = 16
e) 25^x+2 = 1

Answer 1

A) 8^X = 32 >> 2^3X = 2^5 >> 3X= 5>> X=5/3.

B)9^X =1/3 >> 3^2X = 3^-1 >>2X=-1 >>X= -1/2.

C) 2/3 = 8/27 >> 2/3 = (2/3)^3 >>1=(2/3)² >> 1= 4/9. FALSO

D)2^X+4 =16 >> 2^X= 12 >> 2^X =2²*3 >> 3= 2^(X-2). FALSO;

E)25^X +2= 1>>> 25^X=-1>>>5^2X=-1. IMPOSSÍVEL. FALSO.

Answer 2

$a)8^{x} =32 \\ 2^{3x} = 2^{5 \\} \\ 3x=5 \\ x= \frac{5}{3} \\ \\b) 9^x= \frac{1}{3} \\ 3^2^x= 3^{-1} \\ 2x=-1 \\ x=- \frac{1}{2} \\ \\ c) (\frac{2}{3})^x= \frac{8}{27} \\ ( \frac{2}{3})^x= (\frac{2}{3})^3 \\ x=3 \\ \\ d)2^x^+^4=16 \\ 2^x^+^4=2^4 \\ x+4=4 \\ x=0 \\ \\e) 25^x^+^2=1 \\ 25^x^+^2=25^0 \\ x+2=0 \\ x=-2$