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5-x-0-find-x-




Question Number 59164 by hovea cw last updated on 05/May/19
5^x =0  find x
$$\mathrm{5}^{\mathrm{x}} =\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{x} \\ $$
Answered by MJS last updated on 05/May/19
5^x =0 has no solution for x∈R  but:  lim_(x→−∞) 5^x =lim_(x→+∞)  (1/5^x ) =0
$$\mathrm{5}^{{x}} =\mathrm{0}\:\mathrm{has}\:\mathrm{no}\:\mathrm{solution}\:\mathrm{for}\:{x}\in\mathbb{R} \\ $$$$\mathrm{but}: \\ $$$$\underset{{x}\rightarrow−\infty} {\mathrm{lim}5}^{{x}} =\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{5}^{{x}} }\:=\mathrm{0} \\ $$

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