How to change the subject, when the subject you want to know is a power?

Question

If :
R=IP/1-(1+I)^-N

How do I make N the subject when it is a power and it is also a minus power?

Answer 1

IP/R = 1 - 1/(1 + I)^N
1/(1 + I)^N = 1 - IP/R
(1 + I)^N = 1/(1 - IP/R)
Nlog(1 + I) = log(1/(1 - IP/R))
N = (log(1/(1 - IP/R)))/log(1 + I)