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

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Answer 1 · 2017-12-04T23:59:45

$x = \frac{5}{2 - e^{\frac{1}{4}}} \approx 6.9835$ $x=5/(2-e^(1/4))~~6.9835$

$ln (2 x - 5) - ln x = \frac{1}{4}$ $ln(2x-5)-lnx=1/4$

$ln a - ln b = ln (\frac{a}{b})$ $lna-lnb=ln(a/b)$

$ln (\frac{2 x - 5}{x}) = \frac{1}{4}$ $ln((2x-5)/x)=1/4$

Taking antilogarithm:

$e^{ln (\frac{2 x - 5}{x})} = e^{\frac{1}{4}}$ $e^ln((2x-5)/x)=e^(1/4)$

$\frac{2 x - 5}{x} = e^{\frac{1}{4}}$ $(2x-5)/x=e^(1/4)$

$(2 x - 5) = x e^{\frac{1}{4}}$ $(2x-5)=xe^(1/4)$

$2 x - x e^{\frac{1}{4}} = 5$ $2x-xe^(1/4)=5$

$x (2 - e^{\frac{1}{4}}) = 5$ $x(2-e^(1/4))=5$

$x = \frac{5}{2 - e^{\frac{1}{4}}} \approx 6.9835$ $x=5/(2-e^(1/4))~~6.9835$

What is the value of x for which ln(2x−5)−lnx=14ln(2x-5)-lnx=1/4?