Question

Qual o valor da equação exponencial 4.2^x+2^x-1=72

Answer 1

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$4.2^x+2^{x-1}=72 \\ \\ desmembrando \\ \\ 4.2^x+2^x.2^{-1}=72$

colocando em evidência $2^x$

$2^x(4+2^{-1}=72 \\ \\ 2^x(4+ \frac{1}{2} )=72 \\ \\ 2^x( \frac{8+1}{2} )=72 \\ \\ 2^x.( \frac{9}{2} )=72 \\ \\ 2^x=72\div \frac{9}{2} \\ \\ 2^x=\not72^8\times \frac{2}{\not9} \\ \\ 2^x=8\times2 \\ \\ 2^x=16 \\ \\ \not2^x=\not2^4 \\ \\ x=4$

Answer 2

$4\cdot2^x+2^{x-1}=72 \\ 4\cdot2^x+\dfrac{2^x}{2}=72 \\ 2^x\left(4+\dfrac{1}{2}\right)=72 \\ \\ 2^x\cdot\dfrac{9}{2}=72 \\ \\ 2^x=\dfrac{72\cdot2}{9} \\ 2^x=16=2^4\Rightarrow x=4$