Question

Resolva as equações exponenciais:

a) 2^x+3 = 1/128

b) 5^3x+1 = 1/5

c) 9^x-2 = √3

Answer 1

Oi!
a)
${2}^{x + 3} = \frac{1}{128} \\ {2}^{x + 3} = \frac{1}{2^7} \\ {2}^{x + 3} = {2}^{-7} \\ \\ x + 3 = - 7 \\ x = - 7 - 3 \\ \boxed{x = - 10}$

b)${5}^{3x + 1} = \frac{1}{5}\\ {5}^{3x + 1} = {5}^{-1} \\ 3x + 1 = - 1 \\ 3x = - 1 - 1 \\ 3x = - 2 \\ x = \frac{-2}{3}$
c)
${9}^{x - 2} = \sqrt{3} \\ {(3^2)}^{x - 2} = {3}^{\frac{1}{2}} \\ {3}^{2x - 4} = {3}^{\frac{1}{2}} \\ 2x - 4 = \frac{1}{2}} \\ 2(2x - 4) = 1 \\ 4x - 8 = 1 \\ 4x = 1 + 8 \\ 4x = 9 \\ \boxed{x = 9/4}$
Bons estudos.