1. Compare the following functions based on their growth rate. Use the proof and the proper notations to classify them. (a) (2 points) g(x)=log e
3
​
x vs f(x)= ln 2
x
​
(b) (2 points) g(x)=log 2
​
(x!) vs f(x)=ln(1+x 4
) 4
(c) (2 points) g(x)=3x 2
+x 2
log 2
​
x vs f(x)=2000x+log 2
​
(x!) (d) (2 points) g(x)=4 log 2
​
x
vs f(x)=2 x