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Question Number 187336 by Humble last updated on 16/Feb/23

s o l v e f o r x i f

X^{x} ∙ 5^{x} - 5^{2 + x} = 0

Answered by mr W last updated on 16/Feb/23

x^{x} \times 5^{x} - 25 \times 5^{x} = 0

(x^{x} - 25) 5^{x} = 0

5^{x} \neq 0

\Rightarrow x^{x} - 25 = 0

\Rightarrow x^{x} = 25

\Rightarrow x \ln x = \ln 25

\Rightarrow (\ln x) e^{\ln x} = \ln 25

\Rightarrow \ln x = W (\ln 25)

\Rightarrow x = e^{W (\ln 25)} = \frac{\ln 25}{W (\ln 25)}

\approx \frac{\ln 25}{1.086276} \approx 2.96322 ✓

Commented by Humble last updated on 16/Feb/23

E x c e l l e n t s o l u t i o n! t h a n k y o u, s i r

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