Question

função exponenciais :

2^x+2 + 2^x-3 = 132

Answer 1

2^(x+2) + 2^(x-3) = 132

2^x*2^2 + 2^x*2^(-3) = 132

4*2^x + 2^x/8 = 132

(32*2^x + 2^x) / 8 = 132

33*2^x = 132*8

2^x = 132*8/33

2^x = 32

2^x = 2^5

x = 5

Answer 2

Ae Lucas,

aplique uma das propriedades da exponenciação:

$\mathsf{a^{m+n}=a^m\cdot a^n}$

........................................

$\mathsf{2^{x+2}-2^{x-3}=132}\\\mathsf{2^x\cdot2^2-2^x\cdot2^{-3}=132}\\\\\mathsf{4\cdot2^x- \dfrac{1}{2^3}\cdot2^x=132 }\\\\\mathsf{4\cdot2^x- \dfrac{~2^x}{8}=132 }\\\\\mathsf{Vamos~usar~uma~varia\´vel~auxiliar,~fazemos~2^x=y}$

$\mathsf{4\cdot y+\dfrac{y}{8}=132 }\\\\ \mathsf{4y+ \dfrac{y}{8}=132~~(multiplique~8~por~4y~e~por~132) }\\\\ \mathsf{8\cdot4y+y=8\cdot132}\\ \mathsf{32y+y=1.056}\\ \mathsf{33y=1.056}\\\\ \mathsf{y= \dfrac{1.056}{33} }\\\\ \mathsf{y=32}\\\\ \mathsf{2^x=y,~lembra?}\\\\ \mathsf{2^x=32}\\ \mathsf{2^x=2^5}\\ \mathsf{\not2^x=\not2^5}\\\\ \mathsf{x=5}$

Podemos então escrever a solução da equação exponencial acima:

$\huge\boxed{\mathsf{S=\{5\}}}$

Tenha ótimos estudos mano!