Suppose you want to know how long it will take for an investment to double if it is compounded quarterly at 7%.

Use the formula A + P(1+ r/n)^(nt) where A is the amount, P is the initial investment, r is the interest rate, n is the number of times compounded annually and t is the time in years.

2A = A(1 + .07/4)^(4t)

2 = (1.0175)^4t

log 2 + log (1.0175)^(4t)

log 2 = 4t log(1.0175)

log2/log(1.0175) = 4t

t = 10 years