I'm needing a little assistance with this problem, haven't any trouble until this.

A village of 1000 inhabitants increases at a rate of 10% per year. A neighbouring village of 2000 inhabitants decreases at a rate of 5% per year. After how many years will these two villages have the same population?

So I wrote them as two exponential functions and made them equal to each other. Not sure this is how I should do it but it feels right.

$\displaystyle 1000(1.10)^x=2000(0.95)^x$

Then by definition $\displaystyle C^x=y <==> log(y)=x$

Turned them into this

$\displaystyle log(1.1)1000=log(0.95)2000$

then I know it can be turned into this.

$\displaystyle log1000/log1.1=log2000/log0.95$

And now I'm stuck, help!