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The number of real solutions of the equation ({e}^{{x}})=5^{{x

Question

The number of real solutions of the equation $sin (e^{x}) = 5^{x} + 5^{- x}$ is (are)

0

1

2

Infinitely many

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Michael Discussed

The number of real solutions of the equation

sin (e^{x}) = 5^{x} + 5^{- x}

is (are)

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

sin (e^{x})

has a max value of 1.

5^{x} + 5^{- x}

has a max value of 2.

A . M \geq G . M

\Rightarrow \frac{5 ^{x} + 5 ^{- x}}{2} \geq 5^{x} . 5^{- x}

5^{x} + 5^{- x} \geq 2.

∴

There is no point of intersection of both.

∴

No solution.

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Question Text	The number of real solutions of the equation $sin (e^{x}) = 5^{x} + 5^{- x}$ is (are)
Answer Type	Text solution:1
Upvotes	150