Question

If log2 (y + 1) = 2 log2 x + c and y = 3 when x = 2, find y in terms of x.

Answer 1

Hi,

Explanation:

Let's assume k such as c=log2(k)

`log_2(y+1)=2\ log_2(x)+c\\\\log_2(y+1)=2\ log_2(x)+log_2 (k)\\\\log_2(y+1)=log_2(x^2*k)\\\\y+1=x^2*k\\\\if x=2\ then\ y=3:\\\\3+1=2^2*k\\k=1\\\\c=log_2(1)=0\\y+1=x^2*1\\\\\boxed{y=x^2-1}\\`