inverse of function y=5^x

Question

inverse of the function               y=5^x

Answer 1

To find the inverse of a fumction, the first thing you have to do is interchange the roles of x and y. This would leave you with the expression

x = 5^y. Now you need to solve this for y. Everytime you have to solve for a variable that is an exponenet, logarithms have to be used. This can be done in various ways, depending on which logarithm rules you know. The most useful way that will come up later is by just taking the log of both sides, the use the exponent rule andthen divide.

log x = log (5^y)

log x = y*log 5

(log x)/(log 5) = y

 

The other way is to just use the definition of logaritms. The base being raised to the exponent is the same as the base of the logarithm.

x = 5^y is equivalent to y = log(base 5) x.

 

This is less useful than the first way because in problems that you actually have to find values, log, which is log(base 10) is on your calculator while log(base 5) is not.

 

Hope this helped.