Question

Exercício 1. Resolva as equações exponenciais a seguir:
(a) 3^x=81
(b) 8^x+1 = 4^x+2
(c) 2^2x-3 -3 * 2^x-1+4= 0
(d)
$\sqrt{ {4}^{x} }$
= 1/8​

Answer 1

Resposta:

$a) {3}^{4} =3 \times 3 \times 3 \times 3 = 81$

Answer 2

Resposta:

A)

${3}^{x} = 81 \\ {3}^{x} = {3}^{4} \\ x = 4$

B)

${8}^{x + 1} = {4}^{x \times 2} \\ {2}^{ {3}^{(x + 1)} } = {2}^{ {2}^{(x + 2)} } \\ {2}^{3x + 3} = {2}^{2x + 4} \\ 3x + 3 = 2x + 4 \\ x = 1$

C)

${2}^{2x - 3 - 3} \: . \: {2}^{x - 1 + 4} = 0 \\ 2x - 6 + x + 3 = 0 \\ 3x - 3 = 0 \\ 3x = 3 \\ x = 1$

D)

$\sqrt[2]{ {4}^{x} } = \frac{1}{8} \\ {4}^{ \frac{x}{2} } = \frac{1}{ {2}^{ 3} } \\ {2}^{ {2}^{ \frac{x}{2} } } = {2}^{ - 3} \\ 2 \: . \: \frac{x}{2} = - 3 \\ x = - 3$