How do you solve #ln x - ln (1/x) = 2#?

2 Answers
Ananda Dasgupta
Mar 16, 2018

#x=e#

Explanation:

Since #ln(1/x) = - ln x#, the equation becomes

#2 ln x = 2 implies ln x =1#

So

#x=e#

maganbhai P.
Mar 16, 2018

#x=e#

Explanation:

We have,# (1) log_aX=n<=>X=a^n#
#(2)log_a(M/N)=log_aM-log_aN#
Here,
#lnx-ln(1/x)=2#, Applying (2) ,we get
#=>lnx-[ln1-lnx]=2#
#=>lnx-ln1+lnx=2#, where, #ln1=0#
#=>2lnx=2#
#=>lnx=1=>log_ex=1#, Applying (1) ,we get
#=>x=e^1=e#

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