# 0.9 Logarithms

 Page 1 / 4
This module is part of a collection of modules intended for use by preengineering students enrolled in MATH 108 at the University of Texas at El Paso. This module addresses some applications of logarithms in several fields of engineering. Examples are presented.

## Introduction

This module is intended to present some areas of engineering in which logarithms are used. By reading the material and solving the associated problems, you will learn about some important applications of logarithms in engineering.

## Decibels

The decibel ( dB ) is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. The decibel is used for a wide variety of measurements in science and engineering, most prominently in acoustics, electronics, communications, radar, sonar and control systems.

Decibels are frequently used as a means to express the power ratio for physical systems. It is computed by multiplying the factor 10 by the base 10 logarithm of the ratio of the quantities under consideration. Equation (1) shows the computation that is used to express the ratio of two powers using decibels

${L}_{\text{DB}}=\text{10}{\text{log}}_{\text{10}}\left(\frac{{P}_{2}}{{P}_{1}}\right)$

Gain of an Amplifier: We will begin our discussion of decibels with an application in the field of electronics. An amplifier is an electronic device that is capable of boosting the power present in an input signal to produce an output signal with more power. It can be thought of as a black box as shown in Figure 1.

In practical cases, the ratio of the power in the output signal to the power in the input signal is a positive quantity whose value is greater than unity. The decibel measurement of this ratio of power is often called the gain of the amplifier and is given as

$\text{Gain}=\text{10}{\text{log}}_{\text{10}}\left(\frac{{P}_{\text{output}}}{{P}_{\text{input}}}\right)\text{dB}$

Question: An electronic signal is passed through an amplifier. Suppose that the power present in the signal at the input to the amplifier is 10 W. The power present in the signal at the output of the amplifier is 20 W. Express the gain of the amplifier in decibels.

We can use equation (2) to easily express the gain of the amplifier in terms of decibels

$\text{Gain}=\text{10}{\text{log}}_{\text{10}}\left(\frac{\text{20}W}{\text{10}W}\right)=\text{10}{\text{log}}_{\text{10}}\left(2\right)=3\text{.}\text{01}\text{dB}\approx 3\text{dB}$

## Signal to noise ratio

Electrical signals are often corrupted by a random phenomenon known as noise when they are transmitted from one point to another . Because it is impossible to know the exact value of the noise at any point in time, it is often becomes difficult to extract the orignal signal at the receiver without the application of some form of signal processing algorithm such as a filter . The situation is depicted in Figure 2.

A common figure of merit of communication systems is the signal-to-noise ratio . Communication systems that are characterized by high signal-to-noise ratios are in general superior to those that are characterized by low signal-to-noise ratios.

By definition the signal-to-noise ratio or SNR is given as the ratio of the power in a signal divided by the power in the noise that is responsible for corrupting the signal. The signal-to-noise ratio can be expressed in decibels as follows

what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Can someone give me problems that involes radical expressions like area,volume or motion of pendulum with solution  By By By      