The least value of 2 l o g 100 a − l o g a ( 0.0001 ) , a > 1 is Options: A . &nbsp2 B . &nbsp3 C . &nbsp4 D . &nbspNone

Answer: Option C : C 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 ] ≥ 2.2 [ l o g 100 a . l o g a .100 ] 1 2 = 4 [ l o g a a ] 1 2 = 4

The least value of 2log100a−loga(0.0001), a>1 is

Question

The least value of

2 l o g_{100} a - l o g_{a} (0.0001), a > 1

Options:

A . 2

B . 3

C . 4

D . None

Answer: Option C
:
C

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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