What is the value of x for which #ln(2x-5)-lnx=1/4#?

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Answer 1 · 2017-12-04T23:59:45

#x=5/(2-e^(1/4))~~6.9835#

#ln(2x-5)-lnx=1/4#

#lna-lnb=ln(a/b)#

#ln((2x-5)/x)=1/4#

Taking antilogarithm:

#e^ln((2x-5)/x)=e^(1/4)#

#(2x-5)/x=e^(1/4)#

#(2x-5)=xe^(1/4)#

#2x-xe^(1/4)=5#

#x(2-e^(1/4))=5#

#x=5/(2-e^(1/4))~~6.9835#