Question

If $x_i>1\forall iϵN$, then
$lo{g}_{x_2}{x}_1+lo{g}_{x_3}{x}_2+\dots \dots +lo{g}_{x_n}{x}_{n-1}+lo{g}_{x_1}{x}_n$
has the minimum value

• A. 1
• B. 2
• C. None

Answer 1

The correct option is C None

On applying $A.M.\ge G.M.$
$E\ge n(lo{g}_{x_2}{x}_1.lo{g}_{x_3}{x}_2\dots \dots lo{g}_{x_1}{x}_n{)}^{\frac{1}{n}}=n$
Hence the minimum value is n.