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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.



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.


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 DB = 10 log 10 P 2 P 1 size 12{L rSub { size 8{ ital "DB"} } ="10"`"log" rSub { size 8{"10"} } left ( { {P rSub { size 8{2} } } over {P rSub { size 8{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.

Block diagram of an amplifier.

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

Gain = 10 log 10 P output P input dB size 12{ ital "Gain"="10"`"log" rSub { size 8{"10"} } left ( { {P rSub { size 8{ ital "output"} } } over {P rSub { size 8{ ital "input"} } } } right )~ ital "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

Gain = 10 log 10 20 W 10 W = 10 log 10 ( 2 ) = 3 . 01 dB 3 dB size 12{ ital "Gain"="10"`"log" rSub { size 8{"10"} } left ( { {"20"`W} over {"10"`W} } right )="10"`"log" rSub { size 8{"10"} } \( 2 \) =3 "." "01"` ital "dB" approx 3` ital "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.

Communication system with signal processing.

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

Questions & Answers

Black market what is the meaning
Bless Reply
where there is illegal transactions of goods or services. where there illegal goods or services are sold.
Scarcity is the major problem of any economy which is the limited resources an economy has in order to produce its country's unlimited wants/needs. Therefore, scarcity is the key term beyond the study of Economics.
Bature Reply
what is supply
Rahul Reply
Like the demand, the supply demonstrates the quantities that will be  sold at a certain price. But unlike the demand, the supply relationship  shows an upward slope. This means that the higher the price, the higher the  quantity supplied.  Producers supply more at a higher
or we can say that By supply we mean various quantatirs of a commodity which a producer will offer for sale at different possible prices over a given period of time
What is scarcity?
Jubille Reply
having unlimited needs and wants in a world of limited resources
what are the indicator of over population
Accorobatic Reply
Inefficiency of natural resources
Low PCI .
resources are limited and wants are unlimited
limited resources
what product market?
Gayflor Reply
explain demand
Bless Reply
what is economics
Economics is the social science that studies the production, distribution and consumption of goods and services.Economics focuses on the behaviour and interactions of economic agents and how economies work.
Pls what is national income?
demand is the number of buyers. as the price of goods is increase, the buyers will not consider to buy the goods, so the demand will decreases
National Income is the aggregate monetary value of all final goods and services produced in an economy in an year .
Why pecularities of land has no economic significance, What the economic bad, effictive demand?
Demand is a quantity of goods that a consumer is willing to buy at different prices over a given period of time
Define law of demand
what is deadweightloss
francis Reply
deadweight loss is the allocative inefficiency.... when the equilibrium for good or services is not achived.
hii too
how are you all?
I am here been sick but here
may you get well soon Amanda
What are the implications of classical Economics?
What are the implications of classical Economics school of thought?
Dead weight loss is an inefficient allocation of resources, especially through taxation or restrictions.
Classical Economics had an influenced by ancient economic principle and theory.
hello please what is localization of industry
Bless Reply
price is tantalisingly the only factor determining demand which can be analyze the view
Sinit Reply
Price is tantalizingly the only factor determining demand which can be analyze the view
what is scarcity
Sharkdanny Reply
the state of being scarce or in short supply; shortage.
what is meant by an abnormal demand curve?
Samuel Reply
what is microeconomics
Berun Reply
micronomics can be define as that part of Economics that deals with small scale business. e.g. House hold stuff
Micro economics is the study of individuals, households and firms' behavior un decision making and allocation of resources
what is underemployment
Xornam Reply
It is the situation where the available resources are not used to it optimum
state the law of diminishing returns
Bless, the law of diminishing returns state that one point, adding a single worker will result in a decrease of production.
it is a situation where by people are employ but work under their potential
David please go into details kk
Akua pls when you say people alone? what about facilities?
Definition of underemployment. 1 : the condition in which people in a labor force are employed at less than full-time or regular jobs or at jobs inadequate with respect to their training or economic needs
OK that is good
I am new here
what does law of demand says?
with a diagram explain fairy elastic demand
comprehensive answer for public finance is the money that a government has available to spend from taxes and borrowing.
wilflay Reply
what then comprises of public opinion
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
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Source:  OpenStax, Math 1508 (laboratory) engineering applications of precalculus. OpenStax CNX. Aug 24, 2011 Download for free at http://cnx.org/content/col11337/1.3
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