Solve the logarithmic equation for x.

Question

Solve the logarithmic equation for x. (Enter your answers as a comma-separated list.)

log₂(x) + log₂(x − 2) = 3

x =

Answer 1

There is no solution to this equation

Answer 2

x=4

you might be tempted to also say x=-2, but that's not in the domain as you can't take logs of negative numbers

to the base 2, logx +log(x-2)=3

to the base 2, log(x^2-2x) = 3

2^3 = x^2-2x

x^2-2x-8=0

(x-4)(x+2) = 0

x=4,-2, but throw out -2 leaving only x=4