The formula necessary to solve most compound interest problems is 
Example 1
How long would it take for an investment of $3,500 to become $4,200 if it is invested in an account that earns 6% compounded monthly?
Since, in this problem, the variable is in the exponent, logarithms will be used to solve it.
The $3,500 investment would have become $4,200 in about 3.05 years, or just over 3 years and 2 weeks.