Question

The least value of $2lo{g}_{100}a-lo{g}_a\left(0.0001\right),a>1$ is

• A. 2
• B. 3
• C. 4
• D. None

Answer 1

The correct option is C 4

$E=2lo{g}_{100}a-lo{g}_a(100{)}^{-2}$
$=[2lo{g}_{100}a+2lo{g}_{a}100]$
$\ge 2.2[lo{g}_{100}a.lo{g}_a.100{]}^{\frac{1}{2}}$
$=4[lo{g}_{a}a{]}^{\frac{1}{2}}=4$