SOLUTION: solve for n, where: X = ((Y/Z)^(1/n))-1

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: solve for n, where: X = ((Y/Z)^(1/n))-1      Log On


   

Question 1067732: solve for n, where:
X = ((Y/Z)^(1/n))-1
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
X=%28%28Y%2FZ%29%5E%281%2Fn%29%29-1


Just reverse the order of everything done to n.

X%2B1=%28Y%2FZ%29%5E%281%2Fn%29
but from here, the inverse of exponentiation is logarithm.

log%28%28X%2B1%29%29=log%28%28%28Y%2FZ%29%5E%281%2Fn%29%29%29

log%28%28X%2B1%29%29=%281%2Fn%29%2Alog%28%28Y%2FZ%29%29

n%2Alog%28%28X%2B1%29%29=log%28%28Y%2FZ%29%29

n=log%28%28Y%2FZ%29%29%2Flog%28%28X%2B1%29%29