Logarithms Who needs them?

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# Logarithms Who needs them? - PowerPoint PPT Presentation

Logarithms Who needs them?. Prof. Chuck Paulsen Mechanical Engineering Naugatuck Valley Community College. Why am I here in the first place?. I wrote a book Jen Silverman said I should show it at ATOMIC Give a lecture from one of the chapters.

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### LogarithmsWho needs them?

Prof. Chuck Paulsen

Mechanical Engineering

Naugatuck Valley Community College

### Why am I here in the first place?

I wrote a book

Jen Silverman said I should show it at ATOMIC

Give a lecture from one of the chapters

I wrote this book to help students overcome the fear of the math requirements to pursue a STEM education.

What motivated me to write this book?

In November 2008 I had an Eureka moment!

My Eureka Moment

In a piston cylinder system, much like that in your automobile, the relationship of the pressure and volume is given by,

The work to compress the gas is given by,

Substituting the first equation into the second you get,

Here is a Nov 2013 quiz I gave 13 students in my Introduction to Engineering course.

### LogarithmsDo students know what they are?

1 – What is a logarithm?

Results: 1 student got it right.

2 – What are they good for?

Results: No clue!

A Logarithm Defined

The logarithm (log) of a number to a given base is the exponent of the power to which the base must be raised to give the number!

The log of 1000 to the base 10 is 3

If a log is to the base 10 we often call it a common logarithm.

Finding the Logarithm

• Calculator
• Tables

Find log 6 Using Tables

0 is the characteristic

7782 is the mantissa (see next slide)

How a Slide Rule Works

2 x 3 = 6 hooray!

A Natural Logarithm Defined

There is a special number called the Euler number e = 2.7182. The natural logarithm (ln) of a given number to the base e is the exponent of e must be raised to give the given number

The ln of 1000 to the base e is 6.9078

Not nearly as intuitive as the common logarithm

Which logarithm to use?

• Common logarithms are easier to understand and use.
• Natural logs are the results of nearly all calculus calculations describing the laws of nature. For example:
• Finding the length of the path of a projectile.
• The amount of work done by an expanding gas.
• The time required for a heated object to cool.
• The time for a colony of bacteria to increase to a given size.

Thank you

And visit http://stembooks.com