Show that 3x2 log2x2 is Thetax2 log2x is log base 2 of xSol

Show that 3x² + log₂x² is Theta(x²). log₂x is log base 2 of x.

Solution

Answer:

3x2 + log2x2

=> 3x^2 + 2logx --- Here the x^2 is dominating factor , so theta(x^2)

As we know definition of theta notation ,

c1 * g(n) < = f(n) < =c2*g(n)

now , 3x^2 + 2logx < = c2* x^2

Hence proved.