Thread: Economic Development - Logarithms problem

Hi, I'm having a lot of difficulty with this problem because I'm terrible with logs.

Consider two countries, Chairland and Couchia. In year 0, Chairland starts out with a per-capita
income of $100, and this grows at a rate of 2% per year. Couchia starts out with a per-capita income
of $1000, and this grows at a rate of 1% per year.
In how many years will Chairland’s per-capita income catch up with Couchia’s per-capita income?
(decimals are OK).

So my setup was:
x = years
100 * 1.02^x = 1000 * 1.01^x
= 1.02^x = 10 * 1.01^x

I have no idea where to go from here. Could anyone show me what I should do next?

Originally Posted by JoeZYe

So my setup was:
x = years
100 * 1.02^x = 1000 * 1.01^x
= 1.02^x = 10 * 1.01^x

so;


Some important log rules;




So you could have said;
and then taken logs and gotten the same answer...