How do you solve #ln x = 2(ln 1 - ln 11)#?

1 Answer
Jan 17, 2016

#x=1/121#

Explanation:

Divide both sides by #2#.

#(1/2)lnx=ln1-ln11#

Simplify the right hand side using the logarithm rule: #lna-lnb=ln(a/b)#

#(1/2)lnx=ln(1/11)#

Simplify the left hand side using the logarithm rule: #alnx=ln(x^a)#

#ln(x^(1/2))=ln(1/11)#

#lnsqrtx=ln(1/11)#

Thus, since if #lna=lnb#, then #a=b#,

#sqrtx=1/11#

#x=(1/11)^2#

#x=1/121#