Question

cuanto vale x en la operacion
2logx-log(x-16)=2
gracias

Answer 1

$x>0 \wedge x-16>0\\ x>0 \wedge x>16\\ x>16$

$2\log x- \log(x-16)=2 \\ \log x^2- \log(x-16)=2 \\ \log\frac{x^2}{x-16}=2\\ 10^2=\frac{x^2}{x-16}\\ 100=\frac{x^2}{x-16}\\ 100(x-16)=x^2\\ 100x-1600=x^2\\ x^2-100x+1600=0\\ x^2-80x-20x+1600=0\\ x(x-80)-20(x-80)=0\\ (x-20)(x-80)=0\\ x=20 \vee x=80$