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The number of solutions of the equation ...

The number of solutions of the equation `log_(5)tan theta =log_(5)4. log_(4)(3sin theta)"in" [0, 8pi]` is

A

0

B

2

C

4

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`log_(5)tan theta =log_(5)4. log_(4)(3 sin theta)`
`rArr log_(5)tan theta = log_(5) (3 sin theta)`
`rArr tan theta = 3 sin theta`
`rArr sin theta = 0` or ` cos theta=1//3`
`sin theta = 0` is not possible
`therefore cos theta = 1//3`
But `sin theta, tan theta gt 0`
`therefore` for `cos theta = 1//3, theta` lies in the first quadrant only
`therefore` four solutions only
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