Question

resolva as equações exponenciais:
b)8^x+1=32
c)2^x+1=8
d)5^x^2+2x=125
e)3^4-2x=9^2x

Answer 1

a) 4^x = 8 = 2 ^ 2+x = 2 ^ 3 => 2 + x = 3 => x = 1

b) 8 ^ x + 1 = 32 => 2 ^ 3 +x +1 = 2 ^ 5 => 2 ^ x +4 = 2 ^ 5=> x + 4 = 5 => x = 1

c) 2 ^ x +1 = 2^3 => x +1 = 3 => x = 2

d) 5 ^ x^2 +2x = 5^3 => x^2 +2x = 3 => x^2  + 2x - 3 =0 => (usando a fórmula de Baskara {b² -4ac}, obteremos x' = 1 e x'' = -3

e) 3 ^ 4-2x = 9 ^ 2x => 3^4-2x = 3^ 3 + 2x => 4-2x = 2x + 3=> 4x = 1=> x = 1/4