Question

resolva a equação exponrnciais em R:

a) 2^x+1 +2^x-1=40

Answer 1

$2^{x+1}+2^{x-1}=40\\\\2^x\cdot2^1+2^x\cdot2^{-1}=40\\\\2\cdot2^x+\frac{2^x}{2}=40\\\\4\cdot2^x+2^x=80\\\\5\cdot2^x=80\\\\2^x=\frac{80}{5}\\\\2^x=16\\\\2^x=2^4\\\\\boxed{x=4}$

Answer 2

$2^{x+1} + 2^{x-1} = 40$
Vamos fatorar:
$2^{x}(2^1 + 2^{-1}) = 40$
$2^{x}(2 + \frac{1}{2}) = 40$
$2^{x}(\frac{4}{2} + \frac{1}{2}) = 40$
$2^{x}(\frac{5}{2}) = 40$
$2^{x} = \frac{40}{\frac{5}{2}}$
$2^{x} = 40 \frac{2}{5}$
$2^{x} = 16$
Como 16 = 2^4
$2^{x} = 2^4$
$x = 4$