Question

log (x+3) na base 2 = 2 + log (x-5) na base 2

Answer 1

$\log_2(x+3)=2+\log_2(x-5)\\\\\log_2(x+3)=2+\log_2(x-5)\\\\\log_2(x+3)-\log_2(x-5)=2\\\\\log_2\left(\dfrac{x+3}{x-5}\right)=2\\\\\\\dfrac{x+3}{x-5}=2^2\\\\\\\dfrac{x+3}{x-5}=4\\\\x+3=4x-20\\\\x-4x=-3-20\\\\-3x=-23\\\\3x=23\\\\x=\dfrac{23}{3}\\\\\\\\\boxed{S=\left\{\dfrac{23}{3}\right\}}$