SOLUTION: I would like help with this question please (2log base 2 (x-6)) - (log base 2 X)= 3 I am lost.

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Question 634202: I would like help with this question please
(2log base 2 (x-6)) - (log base 2 X)= 3
I am lost.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
(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%28%28x-6%29%5E2%2Fx%29 = 3
:
The exponent equiv of logs
%28x-6%29%5E2%2Fx =2%5E3
Multiply both sides by x
(x-6)^2 = 8x
:
FOIL (x-6)(x-6)
x%5E2-12x%2B36 = 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