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Log and Exponential Functions: Mathematical Preliminaries - Prof. Saumendra Sengupta, Study notes of Data Structures and Algorithms

State University of New York Polytechnic - Utica-RomeData Structures and Algorithms
Prof. Saumendra Sengupta

An introduction to log and exponential functions, including their definitions, typical operations, and the relationship between the two. It covers log base 2, log base e (natural log), and exponential functions, as well as composite functions and their graphical representation.

Typology: Study notes

Pre 2010

Uploaded on 08/09/2009

koofers-user-k1x
koofers-user-k1x 🇺🇸

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bg1
Mathematical preliminaries.
1. A log function is defined as follows:
Tn
2
log
implies
n
T2
. Similarly,
Sm
5
log
implies
m
S5
.
A log function looks like
Typical operations with logs …
a.
xanx
n
a
)(log
b.
)(log)(log)(log yxxy
aaa
c.
)(log)(loglog yx
y
x
aaa
d.
01log
a
irrespective of its base
In CS, we would normally use either the base 2 log
or base e log (natural log).
)(log x
a
pf3

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Download Log and Exponential Functions: Mathematical Preliminaries - Prof. Saumendra Sengupta and more Study notes Data Structures and Algorithms in PDF only on Docsity!

Mathematical preliminaries.

1. A log function is defined as follows:

n log 2 T implies T  2 n. Similarly, m log 5 S implies

S  5 m

A log function looks like

Typical operations with logs …

a. x^ n a x

n log a ()  

b. log^ a^ (xy)^ loga(x)loga(y)

c. log^ y log (x) log (y)

x a  a  a     

d. log^ a^1 ^0 irrespective of its base

In CS, we would normally use either the base 2 log

or base e log (natural log).

log (x )

a

For instance,^24096

and log^2 4096 ^12

If log^ e^ y^2.^3 , we have

y  e 2.^3

where

An exponential function

y  e x

looks like this!

if you take log of an exponential function you get

log e ex x.

The function

y  e x

is never negative.

y=exp(x) x y=exp(-x) x