Find the inverse of the function with a log base of 1/2

Question

The function i need to find the inverse to with a log base of 1/2 is A(t)=500(1/2)^t/272

Answer 1

Let y = 500(1/2)^t/272

Switch y and t to get t = 500(1/2)^y/272

Solve for y: t/500 = (1/2)^y/272

log_1/2(t/500) = y/272

y = 272log_1/2(t/500) = A^-1(t)