Question 634202
(2log base 2 (x-6)) - (log base 2 X)= 3
We can write it
2log2(x-6) - log2(x) = 3
:
we can put the exponent inside log
log2((x-6)^2) - log2(x) = 3
:
Subtraction of logs is divide, we can write it as a single log
{{{log2((x-6)^2/x)}}} = 3
:
The exponent equiv of logs
{{{(x-6)^2/x}}} ={{{2^3}}}
Multiply both sides by x
(x-6)^2 = 8x
:
FOIL (x-6)(x-6)
{{{x^2-12x+36}}} = 8x
:
A quadratic equation
x^2 - 12x - 8x + 36 = 0
x^2 - 20x + 36 = 0
Factors to
(x-18)(x-2) = 0
Two solutions 
x = 2; not a solution x-6 would put a neg inside the log
and 
x = 18 is our solution