The least value of $2 l o g_{100} a - l o g_{a} (0.0001), a > 1$ is

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Solution

The correct option is C 4
$E = 2 l o g_{100} a - l o g_{a} (100)^{- 2}$
$= [2 l o g_{100} a + 2 l o g_{a} 100]$
$\geq 2.2 [l o g_{100} a . l o g_{a} .100]^{\frac{1}{2}}$
$= 4 [l o g_{a} a]^{\frac{1}{2}} = 4$

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