Solve Logarithmic Equation: 3 Solutions Explained

[Essnov]

Homework Statement

I'm trying to solve this logarithmic equation, which has 3 possible solutions. However, I can only get to one of them. What are other ways I can solve it so I get to these other solutions?

Homework Equations

(ln x)^3 = 3 ln x

The Attempt at a Solution

(ln x)^3 = 3 ln x
(ln x)^2 = 3
ln x = sqrt(3)
e^sqrt(3) = x

 

[cristo]

MAke the substitution y=lnx. Then your equation becomes y³-3y=0. Can you solve this for y?

(Note: You don't have to make the substitution; you could do it using your method. Your problems are:

(ln x)^3 = 3 ln x
(ln x)^2 = 3

Here you lost a solution by dividing by lnx

ln x = sqrt(3)

Here you only took one value of the square root)

 

[Essnov]

Thanks a lot.

x = 1, e^sqrt(3), e^-sqrt(3)