Question

${2}^{x + 5} + {2 }^{x + 3} + {2}^{x + 1} = 256$
Calcular "x"
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Answer 1

Respuesta:

Explicación paso a paso:

2^{x+5}+2^{x+3}+2^{x+1}=256\quad :\quad x=\frac{\ln \left(\frac{256}{21}\right)}{\ln \left(2\right)}-1\quad \left(\mathrm{Decimal}:\quad x=2.60768\dots \right)

2^{x+5}+2^{x+3}+2^{x+1}=256

21\cdot \:2^{x+1}=256

2^{x+1}=\frac{256}{21}

Aplicar la ley de expoentes:

\left(x+1\right)\ln \left(2\right)=\ln \left(\frac{256}{21}\right)

=\frac{\ln \left(\frac{256}{21}\right)}{\ln \left(2\right)}-1