Question

Resolva as seguintes equações exponenciais:
a) 4^x=128
b) 3^x+2=81^x-3

Answer 1

Olá,

a)

$\tt \: {4}^{x} = 128 \\ \tt \: {4}^{x} = {4}^{4} \\ \tt \: { \cancel{4}}^{x} = { \cancel{4}}^{4} \\ \boxed{ \tt \: x = 4 }$

b)

$\tt \: {3}^{x + 2} = {81}^{x - 3} \\ \tt \: {3}^{x + 2} = ( {3}^{4} {)}^{x - 3} \\ \tt \: {3}^{x + 2} = {3}^{4x - 12} \\ \tt \: { \cancel{ 3 }}^{x + 2} = { \cancel{3}}^{4x - 12} \\ \tt \: x + 2 = 4x - 12 \\ \tt \: x - 4x = - 12 - 2 \\ \tt \: - 3x = - 14 \\ \tt \: x = \frac{ - 14}{ - 3} \\ \boxed{ \tt \: x = \frac{14}{3} }$