2-x-2-1-3-x-

Question Number 148011 by puissant last updated on 25/Jul/21

2^{(\frac{x}{2})} - 1 = 3^{x}

Commented by mr W last updated on 25/Jul/21

x > 0 :

3^{x} > {(\sqrt{2})}^{x} \Rightarrow 3^{x} - 2^{\frac{x}{2}} > 0 \neq - 1 \Rightarrow n o s o l u t i o n

x = 0 :

3^{x} = {(\sqrt{2})}^{x} \Rightarrow 3^{x} - 2^{\frac{x}{2}} = 0 \neq - 1 \Rightarrow n o s o l u t i o n

x < 0 :

0 < 3^{x} < 1, 0 < {(\sqrt{2})}^{x} < 1

\Rightarrow - 1 < 3^{x} - 2^{\frac{x}{2}} < 1

\Rightarrow 3^{x} - 2^{\frac{x}{2}} \neq - 1 \Rightarrow n o s o l u t i o n

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