How do you solve the equation #(ln x)^2 = (ln x)^3#?

Question

There are two solutions; however, I can only manage to obtain one..

313 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-17T16:19:23

#x=1, e#

We want to find solutions to #(lnx)^2=(lnx)^3#.

First, we bring all terms to one side. We must not divide by any term whose value is unknown.

#(lnx)^3-(lnx)^2=0#

We then factorise the LHS of the equation

#(lnx)^2(lnx-1)=0#

#rArr(lnx)^2=0rArrlnx=0rArrx=1#

#rArrlnx-1=0rArrlnx=1rArrx=e#