Suppose that you deposit your money in a bank that pays interest at a nominal rate of 10% per year. How long will it take for your money to double if the interest rate is compound?
Could you, please, check the correctness of my thoughts?
The condition above may be rephrasing as follows:
find n such that
$A(1+r)^n=2A$
Solution
$2-(1+r)^n=0$
$(1+r)^n=2$
$n=\log_{(1+r)}2$