Q52 / 90 · KVPY 2011 (SB/SX) · Mathematics

Suppose $\log _{a} b+\log _{b} a=c$. The smallest possible integer value of $c$ for all $a, b>1$ is -

A
4
B
3
Correct answer
C
2
D
1

Solution

$\mathrm{c}=\log _{\mathrm{a}} \mathrm{b}+\frac{1}{\log _{\mathrm{a}} \mathrm{b}} \geq 2$

Hence, the correct answer is option: 'C'.

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