Logarithms question

1. Nov 8, 2013

Coco12

1. The problem statement, all variables and given/known data

Log(2x-3)=log(4x-3)-logx
2. Relevant equations

Logcl =logcr
L=r

3. The attempt at a solution
Quotient law of logs

So I simplfied:
Log(2x-3)=log(4x-3)/x

Since same base:
2x-3=4x-3/x

2x^2-7x+3=0
(X-1)(x-6)

The ans is supposed to be 3. I don't know what I'm doing wrong?

Last edited: Nov 8, 2013
2. Nov 8, 2013

ar1994

Have you double checked your algebra? After you've removed the logarithms and come up with the algebraic equation, are you sure you manipulated it into a polynomial correctly?

3. Nov 8, 2013

Staff: Mentor

First it was log(2x + 5), but now it's log(2x + 3). Which one is it?
For the equation you posted, 3 is not a solution. Here's the check:
If x = 3,
log(11) =? log(9) - log(3)
log(11) =? log(9/3) = log(3)
Since log(11) ≠ log(3), 3 is not a solution.

In your work you need a few more parentheses.
In the two equations above, log(4x-3)/x should be written as log[(4x - 3)/x], and 4x -3/x is not the same as (4x - 3)/x.
In what you have above, you started with an equation, but lost the = 0, so you're not working with equations any more.

Have you copied the equation correctly? If so, did you look at the right solution? There's also the possibility that the answer in your book is wrong.

4. Nov 8, 2013

Coco12

Ya it's supposed to be 2x-3. That is what the book says.. That the ans is 3.

I think 3 is right. Because when I plugged in into the equation, I got it..

However how did they get that?

Last edited: Nov 8, 2013
5. Nov 8, 2013

Staff: Mentor

Which is different from either of the two expressions you had before. You need to be more careful!
No.
Just before you did the factoring, you had 2x2 - 7x + 3, which is correct as far as it goes.

It should be 2x2 - 7x + 3 = 0.

Try again on the factorization.

You will also need to consider the domain for each individual log expression.
What are the restrictions on x so that log(2x - 3) is defined?
What are the restrictions on x so that log(4x - 3) is defined?
What are the restrictions on x so that log(x) is defined?

Your solution has to be in an interval for what all three log expressions are defined.

6. Nov 8, 2013

ar1994

Even if it is supposed to be 2x-3, you're factorization is still incorrect. To see why, simply try plugging in the roots you found back into the logarithmic equation, as Mark44 suggested, or even in the polynomial from which you obtained the roots. You will find that they do not satisfy the equation.