Let a =2010 log 2011 2012, b =2010 log 2012 2011 and c =(2010)2 then which one of the following is the most appropriate altemative?

Question

Let a =2010 log 2011 2012, b =2010 log 2012 2011 and c =(2010)2 then which one of the following is the most appropriate altemative? (A) a b=c (B) a b >c (C) a b ≥ c (D) a b ≤ c

Tardigrade Admin · Accepted Answer

a ⋅ b=2010( log 2011 2012+ log 2012 2011) (y+(1/y) ≥ 2, y>0) Now, log 2011 2012+ log 2012 2011>2 (Θ log 2011 2012>0, ≠ 1) ∴ ab > c

Q. Let $a = 201 0^{l o g_{2011} 2012}, b = 201 0^{l o g_{2012} 2011}$ and $c = (2010)^{2}$ then which one of the following is the most appropriate altemative?

$ab = c$

$ab > c$

$ab \geq c$

$ab \leq c$

$a \cdot b = 201 0^{(l o g_{2011} 2012 + l o g_{2012} 2011)} (y + \frac{1}{y} \geq 2, y > 0)$
Now, $lo g_{2011} 2012 + lo g_{2012} 2011 > 2 (Θ lo g_{2011} 2012 > 0, \neq = 1)$
$∴ ab > c$

Q. Let a=2010log2011​2012,b=2010log2012​2011 and c=(2010)2 then which one of the following is the most appropriate altemative?

ab=c

ab>c

ab≥c

ab≤c