The number of solutions of the equation $s i n (e^{x}) = 5^{x} + 5^{- x}$ is

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infinitely many

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Solution

The correct option is B 0
$s i n (e^{x}) = 5 x + 5^{- x}, l e t 5^{x} = t, t h e n s i n (e^{x}) = t + \frac{1}{t} = (\sqrt{t} - \frac{1}{\sqrt{t}}) + 2 [∵ 5^{x} > 0] \Rightarrow s i n (e^{x}) \geq 2$ , which is not possible for any real $x$ .

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