Thread: Log System of equations

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.

Then by definition

Turned them into this

then I know it can be turned into this.


And now I'm stuck, help!

Originally Posted by Gerard

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.

To make things easier, divide both sides by 1000.

What next?

Originally Posted by pickslides

To make things easier, divide both sides by 1000.

What next?

Then using the definition...



?

Using what definition? Taking the logarithm of both sides (any base) of
you get

x log(1.1)= x log(.95)+ log 2