logarithms

For positive non-zero real variables x and y, if $\ln\left(\frac{x+y}{2}\right) = \frac{1}{2}[\ln (x) + \ln (y)]$ then, the value of $\frac{x}{y} + \frac{y}{x}$ is

For positive non-zero real variables p and q, if log (p² + q²) = log p + log q + 2 log 3, then, the value of $\frac{p^4+q^4}{p^2q^2}$ is

For positive non-zero real variables $p$ and $q$, if $\log \left(p^2 + q^2\right) = \log p + \log q + 2 \log 3$, then, the value of $\frac{p^4 + q^4}{p^2 q^2}$ is

For positive non-zero real variables $x$ and $y$, if $\ln \left( \frac{x + y}{2} \right) = \frac{1}{2} [ \ln (x) + \ln (y) ]$ then, the value of $\frac{x}{y} + \frac{y}{x}$ is

Consider the following three functions. f 1 = 10 n , f 2 = n logn , f 3 = n √n Which one of the following options arranges the functions in the increasing order of asymptotic growt...

Let S denote the set of all functions $$f:\,{\{ 0,\,1\} ^4}\, \to \,\{ 0,\,1\} $$. Denote by N the number of functions from S to the set {0, 1}. The value of $${\log _2}$$ $${\log...

The worst case running time to search for an element in a balanced binary search tree with n2 n elements is

Two alternate packages A and B are available for processing a database having 10 k records. Package A requires 0.0001n 2 time units and package B requires $$10n.\log _{10}^n$$ time...

Consider the following functions $$f(n) = 3{n^{\sqrt n }}$$ $$g(n) = {2^{\sqrt n {{\log }_2}n}}$$ $$h(n) = n!$$ Which of the following is true?