Given 𝑙𝑜𝑔2𝑛
Let
F(n)=𝑙𝑜𝑔2𝑛
n=4n
F(4n) = 𝑙𝑜𝑔24𝑛
F(4n) = 𝑙𝑜𝑔24 +𝑙𝑜𝑔2𝑛
F(4n) = 𝑙𝑜𝑔22∗2 +F(n)
F(4n) = 2𝑙𝑜𝑔22 + F(n)
F(4n) = 2+ F(n)
Finally,
F(4n) = 2+𝑙𝑜𝑔2𝑛
Given √𝑛
Let,
F(n)=√𝑛
F(4n)=√4𝑛
F(4n)=2√𝑛
F(4n)=2* F(n)
Given n
Let,
F(n)=n
F(4n)=4n
F(4n)=4* F(n)
Given n2
Let,
F(n)=n2
F(4n)=(4n)2
F(4n)=16*n2
F(4n)=16* F(n)
Given n3
Let,
F(n)=n3
F(4n)=(4n)3
F(4n)=64* n3
F(4n)=64* F(n)
Given 2n
Let,
F(n)=2n
F(4n)=24n
F(4n)=(2n)4
F(4n)= (F(n))4