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

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Answer 1 · 2016-01-17T04:35:57

#x=1/121#

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#