Question Number 215808 by efronzo1 last updated on 19/Jan/25
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Answered by golsendro last updated on 19/Jan/25
$$\:\:=\:\mathrm{e}^{\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\frac{{a}^{{x}} +{b}^{{x}} +{c}^{{x}} −\mathrm{3}}{{x}}\right)} \\ $$$$\:\:\:=\:{e}^{\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left(\mathrm{ln}\:{a}\:.{a}^{{x}} +\:\mathrm{ln}\:{b}.\:{b}^{{x}} +\:\mathrm{ln}\:{c}.\:{c}^{{x}} \right)} \\ $$$$\:\:\:=\:{e}^{\mathrm{ln}\:\left({abc}\right)} \:=\:\mathrm{8}\: \\ $$