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

Question Number 148048 by puissant last updated on 25/Jul/21

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

Answered by mindispower last updated on 25/Jul/21

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

\Leftrightarrow 1 = {(\frac{1}{2})}^{x} + {(\frac{\sqrt{3}}{2})}^{x}

x = 2 s o l u t i o n

i f x ⩽ 0, {(\frac{1}{2})}^{x} + {(\frac{\sqrt{3}}{2})}^{x} ⩾ 2

x \to {(\frac{1}{2})}^{x} + {(\frac{\sqrt{3}}{2})}^{x} d e c r e a s e f u n c t i o n f o r x > 0

f (2) = 1, \Rightarrow x = 2

Answered by Rasheed.Sindhi last updated on 25/Jul/21

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

2^{2 y} - 3^{y} = 1 [x / 2 \to y]

4^{y} - 3^{y} = 1

y > 1 \Rightarrow 4^{y} - 3^{y} > 1

y > 1 \Rightarrow x / 2 > 1 \to N o s o l u t i o n

y = 1 \Rightarrow x = 2