Question

Resolva as seguintes equações exponenciais:
a) 2^x = 64
b) 3^2x = 1/9
c) 8^x+1 = 4^x-3

Answer 1

Resposta:

a)

${2}^{x} = 64$

${2}^{x} = {2}^{6}$

$x = 6$

b)

${3}^{2x} = \frac{1}{9}$

${3}^{2x} = \frac{1}{ {3}^{2} }$

${3}^{2x} = {3}^{ - 2}$

$2x = - 2$

$x = \frac{ - 2}{2}$

$x = - 1$

c)

${8}^{x + 1} = {4}^{x - 3}$

${( {2}^{3} )}^{x + 1} = {( {2}^{2} )}^{x - 3}$

${2}^{3 \cdot(x + 1)} = {2}^{2 \cdot(x - 3)}$

${2}^{3x + 3} = {2}^{2x - 6}$

$3x + 3 = 2x - 6$

$3x - 2x = - 6 - 3$

$x = - 9$