Question

How do you solve `log_2(x^2 - 2x) =3`?

Answer 1

Take the exponential base `2` of both sides, then solve the resulting quadratic to find:

`x=4` or `x = -2`

Explanation:

Take the exponential base `2` of both sides:

`x^2-2x = 2^(log_2(x^2-2x)) = 2^3 = 8`

Subtract `8` from both ends to get:

`0 = x^2-2x-8 = (x-4)(x+2)`

So `x=4` or `x=-2`