If you haven ' t learned about logarithms , then you can only solve this using trial and error . Logarithms are the inverse functions of exponents . Similar to the idea of how multiplication and division are inverses of each other . For example , lets take the case of 4 2 t Here , the obvious answer would be that t 2 . For your case , you can at least simplify the equation by dividing through by 500 which would yield the equation 2 1 . 07 tWith logarithms , you would take the log of both sides and it would look something like this . log 2 log 1 . 07 t t log 1 . 07 Thus , t log 2 log 1 . 07 Logs can have different bases though , and the 2 that are most commonly used at log 10 usually represented as log and loge usually represented as ln .