# Math Help - Natural log equations question

1. ## Natural log equations question

The equation 3lnx=lb3x is solved by the sqaure root of 3.

Thanks

2. ## Re: Natural log equations question

3ln(x) = ln(3x)

ln(x3) = ln(3x)

x3 = 3x

x3 - 3x = 0

x (x2 - 3) = 0

x = 0 or else x2 - 3 = 0

Edited...

4. ## Re: Natural log equations question

Originally Posted by tom@ballooncalculus
3ln(x) = ln(3x)

ln(x3) = ln(3x)

x3 = 3x

x3 - 3x = 0

x (x2 - 3) = 0

x = 0 or else x2 - 3 = 0
Note that \displaystyle \begin{align*} x = 0 \end{align*} and \displaystyle \begin{align*} x = -\sqrt{3} \end{align*} are NOT acceptable solutions, because \displaystyle \begin{align*} \ln{x} \end{align*} is only defined for \displaystyle \begin{align*} x > 0 \end{align*}.