# How do you solve #Ln e^x = 5#?

##### 1 Answer

Aug 16, 2016

Real solution:

Complex solutions:

#### Explanation:

The only Real value of

The function

The function

So for any

If we consider Complex solutions, note that

Hence we find solutions:

#x = 5 + 2kpii " "# for any integer#k#

since:

#ln e^(5+2kpii) = ln (e^5 e^(2kpii)) = ln(e^5 * (e^(2pii))^k) = ln (e^5*1^k) = ln e^5 = 5#