The number of solution of \( \Large \frac{log 5 + log \left(x^{2}+1\right) }{log \left(x-2\right) }=2 \)

A) 2

B) 3

C) 1

D) none of these

Correct answer:
D) none of these

Description for Correct answer:

We have, \( \Large \frac{log5 + log \left(x^{2}+1\right) }{log \left(x-2\right) } = 2 \)

=> \( \Large log\{ 5 \left(x^{2}+1\right) \} = log \left(x-2\right)^{2} \)

=> \( \Large 5  \left(x^{2}+1\right)= \left(x-2\right)^{2}=4x^{2}+4x+1=0 \)

=> \( \Large x = -\frac{1}{2} \)

But for \( \Large x = -\frac{1}{2},\ log \left(x-z\right) \) is not meaningful, it has no root.



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