Question

Resolva a seguinte equação exponencial:
$2^x + 2^x^+^1+2^x^+^2+2^x^+^3=15/2$

Answer 1

$2^{x}+2^{x+1}+2^{x+2}+2^{x+3}=\dfrac{15}{2}$

$2^{x}+2\cdot2^{x}+2^2\cdot2^{x}+2^3\cdot2^{x}=\dfrac{15}{2}$

$2^{x}\cdot(1+2+2^2+2^3)=\dfrac{15}{2}$

$2^{x}\cdot(1+2+4+8)=\dfrac{15}{2}$

$2^{x}\cdot15=\dfrac{15}{2}$

$2^{x}=\dfrac{\frac{15}{2}}{15}$

$2^{x}=\dfrac{15}{2}\cdot\dfrac{1}{15}$

$2^{x}=\dfrac{1}{2}$

$2^{x}=2^{-1}$

$x=-1$

$S=\{-1\}$