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Question

The number of value(s) of θ[0,2π] satisfying the equation (log5tanθ)logtanθ55+log555=6 is

A
0
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B
4
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C
2
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D
5
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Solution

The correct option is C 2
(log5tanθ)logtanθ55+log555=6
log5tanθ3log5tanθ+3=6
Put x=log5tanθ
Then, x3x+3=6 (1)
xx+1x=2
x2+x2=0, x0
(x+2)(x1)=0
x=1,2

But from (1), we can conclude x<0
x=2
log5tanθ=2
tanθ=15
As θ[0,2π], there are two solutions.

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