Question-20132

Question Number 20132 by mondodotto@gmail.com last updated on 22/Aug/17

Answered by mrW1 last updated on 22/Aug/17

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

x^{2} = 10^{\frac{x}{25}}

x = \pm 10^{\frac{x}{50}}

50 \times \frac{x}{50} = \pm 10^{\frac{x}{50}}

50 t = \pm 10^{t} with t = \frac{x}{50}

50 t = \pm e^{tln 10}

{50 te}^{- tln 10} = \pm 1

(- tln 10) e^{- tln 10} = \pm \frac{\ln 10}{50}

\Rightarrow - tln 10 = W (\pm \frac{\ln 10}{50})

\Rightarrow t = - \frac{1}{\ln 10} W (\pm \frac{\ln 10}{50})

\Rightarrow x = - \frac{50}{\ln 10} W (\pm \frac{\ln 10}{50})

= {\begin{cases} - \frac{50}{\ln 10} W (\frac{\ln 10}{50}) = - 0.95698 \\ - \frac{50}{\ln 10} W (- \frac{\ln 10}{50}) = {\begin{cases} 1.05952 \\ 100 \end{cases} \end{cases}

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