Finding the inverse of a logarithmic equation

Question

Find the inverse of the function A(t)=500(1/2)↑ t/272. I can't use natural log to find the answer and I don't know how to solve for the inverse without using natural log

Answer 1

A/500 = 2^-t/272

why can't ln=natural log be used?

ln(A/500)=(-t/272)ln(2)

t=(-272)*[lnA-ln500]/ln2

Answer 2

Are you prohibited from using log base 10 or log base 2? The inverse of a exponential function involves a logarithm in some way. If you are merely using the inverse to solve a problem - most multiple choice problems give you some power of 1/2 for A/500 and it's easy to pick off the t as a multiple of the time constant, 272.

Anyway, using log base 10

A/500 = 2^-t/272

log(A/500) = -(t/272)log2

-272log(A/500)/log2 = t