For the following, use the inverse relationship between logarithms and exponentials to determine x.

Question

log2(x^2−2x)=3
Solution Set:_____________?

I don't know how to do this question at all :( Please help and show the work as well so that I can learn! Thanks.

Answer 1

log2(x^2−2x)=3
by definition
x^2 - 2x = 2^3
x^2 - 2x - 8 = 0
(x-4)(x+2) = 0
x = 4 or x + -2

testing:
if x=4
log₂ (16 -16) = 3
log₂ 0 = 3 , which is not true since log 0 is undefined

if x = -2
log₂ (4 + 4) = 3
log₂ (8) = 3 , which is true

so x = -2