solve-for-x-if-log-x-x-2-25-

Question Number 189610 by Spillover last updated on 19/Mar/23

s o l v e f o r x i f

\log x = \frac{x^{2}}{25}

Answered by mr W last updated on 19/Mar/23

\ln x = \frac{x^{2}}{25} = \frac{e^{2 \ln x}}{25}

(\ln x) e^{- 2 \ln x} = \frac{1}{25}

(- 2 \ln x) e^{- 2 \ln x} = - \frac{2}{25}

- 2 \ln x = W (- \frac{2}{25})

\ln x = - \frac{1}{2} W (- \frac{2}{25})

\Rightarrow x = e^{- \frac{1}{2} W (- \frac{2}{25})}

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