Question

Qual a resolução para 8^x-9=(1/2)^x+1

Answer 1

$8^{x-9}=(\frac{1}{2})^{x+1}\\\\(2^{3})^{x-9}=\frac{1^{x+1}}{2^{x+1}}\\\\2^{3(x-9)}=\frac{1}{2^{x+1}}\\\\2^{3x-27}=2^{-(x+1)}\\\\\\3x-27=-(x+1)\\\\3x=-x-1+27\\\\3x+x=26\\\\4x=26\\\\x=\frac{26}{4}\\\\x=\frac{13}{2}~~ou~~6,5$

Answer 2

Boa Noite

8⁽ˣ ⁻ ⁹⁾ = (1/2)⁽ˣ ⁺ ¹⁾
2³⁽ˣ ⁻ ⁹⁾ = 2⁻¹⁽ˣ ⁺ ¹⁾
2⁽³ˣ ⁻ ²⁷⁾ = 2⁽⁻ˣ ⁻ ¹⁾

Bases iguais, expoentes iguais

3x - 27 = -x -1
3x + x = -1 + 27
4x = 26
x = 26/4
x = 13/2

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