SOLUTION: This equation is giving me issues. log(base2)(x-6)+log(base2)(x-4)-log(base2)x = 2 Solve for x. Reject any value of x that produces the logarithm of a negative number or 0. Wh

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Question 5994: This equation is giving me issues.
log(base2)(x-6)+log(base2)(x-4)-log(base2)x = 2
Solve for x. Reject any value of x that produces the logarithm of a negative number or 0.
What I've done:
log(base2)(x-6)(x-4)-log(base2)x = 2
log(base2)(x-6)(x-4)/x = 2
(x-6)(x-4)/x = 2^2 = 4
4 = (x-6)(x-4)/x
There is where I am stuck.
Some help on this would be great. Thanks.
Found 2 solutions by prince_abubu, MathTherapy:
Answer by prince_abubu(198) (Show Source):
You can put this solution on YOUR website!
So I take it you're stuck at .

All you'll do is cross-multiply. It might be easier if we put it this way:

Then we'll get

<----- We switched the places of the expressions on both sides of the equals sign, and then moved the 4x to the other side so that everything equals zero.

<----- We expanded by using the product by using FOIL.

<--- Combined like terms

<---- Refactored ("UnFoiled")

From looking at your above equation, x = 12 or x = 2.

Answer by MathTherapy(10699) (Show Source):
You can put this solution on YOUR website!

This equation is giving me issues. log(base2)(x-6)+log(base2)(x-4)-log(base2)x = 2 Solve for x. Reject any value of x that produces the logarithm of a negative number or 0. What I've done: log(base2)(x-6)(x-4)-log(base2)x = 2 log(base2)(x-6)(x-4)/x = 2 (x-6)(x-4)/x = 2^2 = 4 4 = (x-6)(x-4)/x There is where I am stuck. Some help on this would be great. Thanks. The person who responded is PARTIALLY WRONG!! The smallest of the 3 logs is x - 6, so x - 6 MUST be > 0, and so, x > 6. So, we get: , with x > 6 The person who responded has solutions, x = 12 and x = 2, but as you can see, the x value, 12 is > 6, but the other value 2, is NOT, thereby making the solution, x = 12, ACCEPTABLE, and x = 2, EXTRANEOUS, and UNACCEPTABLE! The person must've missed this: Reject any value of x that produces the logarithm of a negative number or 0.