Question

Equação exponencial alguém poderia reouver e explicar passo a passo
2^{x+1}+2^x+2^{^{x-1}}-2^{x+2}+2^{x+3}=120

Answer 1

Resposta:

$2^{x+1}+2^x+2^{^{x-1}}-2^{x+2}+2^{x+3}=120 \\ 2^{x}.2+2^x+ \frac{2^{x}}{2} -2^{x}. {2}^{2} +2^{x}. {2}^{3} =120 \\ {2}^{x} ( 2+1+ \frac{1}{2} - {2}^{2} + {2}^{3} ) = 120 \\ {2}^{x} ( 3+ \frac{1}{2} - 4+ 8 ) = 120 \\ {2}^{x} ( 7+ \frac{1}{2} ) = 120 \\ {2}^{x} ( \frac{15 }{2} ) = 120 \\{2}^{x} = 120 . \frac{2 }{15}\\{2}^{x} = 8.2 \\{2}^{x} = 2.2.2.2\\{2}^{x} = {2}^{4} \\ x = 4$