Question

Qual o valor da soma das soluções da equação abaixo?

(log2 x)^2 -6 = log2 x

precisa de calculo!

Answer 1

Resposta:

$\frac{33}{4}$

Explicação passo-a-passo:

$(log_2x)^2-log_2x-6=0\\\\\Delta=(-1)^2-4.1.(-6)\\\\\Delta=1+24\\\\\Delta=25\\\\log_2x=\frac{-(-1)-5}{2.1} \\\\log_2x=\frac{1-5}{2}\\\\log_2x=\frac{-4}{2} \\\\log_2x=-2\\\\x=2^-^2\\\\x=(\frac{1}{2} )^2\\\\x=\frac{1}{4} \\\\log_2x=log_2x=\frac{-(-1)+5}{2.1}\\\\log_2x=\frac{1+5}{2}\\\\log_2x=\frac{6}{2}\\\\log_2x=3\\\\x=2^3\\x=8\\\\\frac{1}{4}+8=\frac{33}{4}$