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The number of distnct real roots of the ...

The number of distnct real roots of the equation `x=((5pi)/(2))^(cos x)`

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
D
We have `x=((5pi)/(2))^(cos x)`
`therefore log_((5pi)/(2))x=cos x`
If `log_((5pi)/(2))x=1`
`therefore x=(5pi)/(2)`
Thus, graph of `y=log_((5pi)/(2))x` passes through the point `((5pi)/(2),1)`
`therefore` Draw the graph of `y=log_((5pi)/(2))x` and y = cos x as shown in the following figure.

From the graph, there are 3 solutions.
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