Question

resolva as seguintes equações exponenciais​

Answer 1

Resposta:

a)

$\sf 2^x =128$   ←   128 na base 2.

$\sf 2^x = 2^7$      ← Cancela a base 2.

$\framebox{ \boldsymbol{ \sf \displaystyle x = 7 }} \quad \gets \mathbf{ Resposta }$

b)

$\sf 3^{2x} = 243$    ← 243 na base 3.

$\sf 3^{2x} = 3^5$      ← Cancela a base 3.

$\sf 2x = 5$

$\framebox{ \boldsymbol{ \sf \displaystyle x = \dfrac{5}{2} }} \quad \gets \mathbf{ Resposta }$

c)

$\sf 2^{x - 2} = 8$

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

$\sf x - 2 = 3$

$\sf x = 3 + 2$

$\framebox{ \boldsymbol{ \sf \displaystyle x = 5 }} \quad \gets \mathbf{ Resposta }$

d)

$\sf 3^{x^{2} - 5} = 81$

$\sf 3^{x^{2} - 5} = 3^4$

$\sf x^{2} - 5 = 4$

$\sf x^{2} = 4 + 5$

$\sf x^{2} = 9$

$\sf x = \pm \sqrt{9}$

$\sf x= \pm 3$

$\framebox{ \boldsymbol{ \sf \displaystyle x_1 = 3 }} \quad \gets \mathbf{ Resposta }$

$\framebox{ \boldsymbol{ \sf \displaystyle x_2 = - \; 3 }} \quad \gets \mathbf{ Resposta }$

e)

$\sf 4^x = 512$

$\sf (2^2)^{\;x} = 2^9$

$\sf 2^{2x} = 2^9$

$\sf 2x = 9$

$\framebox{ \boldsymbol{ \sf \displaystyle x = \dfrac{9}{2} }} \quad \gets \mathbf{ Resposta }$

f)

$\sf 8^x =\dfrac{1}{16}$

$\sf 8^x = 16 ^{-\, 1}$

$\sf {(2^3)}^{x} = {(2^4)}^{-\,1}$

$\sf 2^{3x} = 2^{-\,4}$

$\sf 3x = - 4$

$\framebox{ \boldsymbol{ \sf \displaystyle x = - \,\dfrac{4}{3} }} \quad \gets \mathbf{ Resposta }$

Explicação passo-a-passo: