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Algebra Level 3

sin ⁡ ( e x ) = 5 x + 1 5 x \large \sin (e^x) = 5^x+ \frac 1{5^x}

How many solutions of x x satisfy the equation above?

0 3 2 Infinitely Many

Aniruddha Bagchi by Aniruddha Bagchi , 20, India

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1 solution

Aniruddha Bagchi
May 25, 2017

Using AM-GM Inequality, We see that 5 x 5^x +1/ 5 x 5^x can have a minimum value of 2.

But s i n ( e x ) sin(e^x) can have a maximum value of 1 because the range of any sine function lies from -1 to +1 both inclusive. So if we plot both LHS and RHS sides of the equation on graph we get no common intersections hence no solutions.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Use AM-GM inequality to RHS it will be easy

Kushal Bose - 4 years ago

Did that only ... see the first line of my solution.

Aniruddha Bagchi - 4 years ago

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Oh I missed out that

Kushal Bose - 4 years ago

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