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Question

The equation x(log3x)292log3x+5=33 has

A
at least one real root
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B
exactly one real root
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C
exactly one irrational root
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D
complex roots
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Solution

The correct options are
A at least one real root
C exactly one irrational root
Let log3x=tx=3t
Then (3t)t292t+5=33
3t392t2+5t=332
t392t2+5t=32
2t39t2+10t3=0
(t12)(t1)(t3)=0
t=12,1,3

x=3,3,27 are the roots of the given equation.

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