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:

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

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

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

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

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

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

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