# Logarithm with different base

1. Aug 13, 2009

### songoku

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

I need help for this problem :

If $$2*\log_2 (x-2y)=\log_3 (xy)$$ , find $$\frac{x}{y}$$

2. Relevant equations
$$\log_bx = \frac{\log_ax}{\log_ab}$$

3. The attempt at a solution
$$2*\log_2 (x-2y)=\log_3 (xy)$$

$$\log_2 (x-2y)^2=\log_3 (xy)$$

$$\frac{\log_2 (x-2y)^2}{\log_2 2}=\frac{\log_2 (xy)}{\log_2 3}$$

$$\log_2 (x-2y)^2 * \log_2 3 = \log_2 (xy)$$

Then, I stuck .....

Thx :)

2. Aug 14, 2009

### rock.freak667

Are you sure you wrote the question down correctly? I ask because log23 is not an integer and you be basically computing (x-2y)k=xy where k is not an integer (so you'd not be able to find x/y)

3. Aug 14, 2009

### songoku

Hi rock.freak667

At least that's the whole question that was given to me by my friend. Your post assure me that this question can't be solved.

Thx a lot for pointing out that $$\log_2 3$$ is not an integer