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getting ready for university engineering :(

hey guys, so iv finished my level three engineering in college and i am going to university now, there are a few different things i struggle with though and i would ask for a simple explanation on this site. the biggest of which is how log works and why it is needed. i have looked up videos on the subject but i cant see why it is needed, as far as i understand it is for finding the needed power to connect two numbers together, but there must be more to it than that im sure i am wrong. thank you for any help given.

Reply 1

B_9710

If you have

2^x =3

how are you going to solve it? You have to take logs to solve it which you can put in on a calculator to give you an approximation.
The answer to the above equation is

\log_2 3

.
I'm not sure if I understand your question.

Reply 2

Brandork__135

Original post by B_9710

If you have

2^x =3

how are you going to solve it? You have to take logs to solve it which you can put in on a calculator to give you an approximation.
The answer to the above equation is

\log_2 3

.
I'm not sure if I understand your question.

so the log simply finds the missing power in an equation, thank you, but i dont understand where this would be used in the real world. log has just been something that has been a grey area for some time as all we were told about it in college was it used to be used instead of calculators. but i cant see how.

anyway that you very much for the help dude.

Reply 3

The_Big_E

Original post by Brandork__135

There are a lot of examples of exponentiation and logarithms in the real world. When it comes to engineering, you have things like:

Decibels - A logarithmic unit for measuring intensity of sounds.
Richter scale - A base-10 logarithmic scale for measuring the magnitude of tectonic events such as earthquakes, tsunamis, volcanic eruptions.

Things like bacteria growth, population growth, radioactive decay, interest rates and capacitor charging/discharging are all exponential, and can be modelled with exponential curves.

You can use logarithms to find useful values like the half-life of a radioactive isotope or the time constant of a capacitor.

You will definitely need logarithms for any engineering course.

(edited 7 years ago)

Reply 4

Paulxo

The reason logarithms were discovered/invented was to do calculations like multiplication and division in a fast way. They were used in this way from 1614 to around 1975. The word 'logarithm' contains the word 'arithmetic' which was their intended use. After 1975 people used calculators and computers instead. As a result, many people then understood logarithms as they had used them so much, but these days it's a bit of a leap to use them as they seemingly come from nowhere. How they work is that the tell you what power you need to make a number, eg.

What power do I need to make 10 become 37?
In other words, I know I'll need a power between 1 and 2 and 10^1 = 10 and 10^2 = 100.

What is it? 1.568

So that means that 10^1.568 = 37

What's the point of this? To use it for multiplying (or dividing). Let's say you wanted - as a simple example - to multiply 37 by itself. Instead of doing that you can just replace 37 x 37 with

10^1.568 x 10^1.568 = 10^3.136

You can look up the value of 3.136 in a table that was already figured out.

This would give 1369.

So it turns what could be a complicated multiplication into a simple addition and then you just look up the answers. Google 'log tables' and look up 0.136.

The slide rule was invented using this method also, and enabled you to do things like 14 x 21 or 1.4 x 0.21. This is explained in this video.
http://www.youtube.com/watch?v=XDVdomiS6fI

As already mentioned, logs unpick what powers are required, so they are the reverse of indices. Everything in maths has a reverse so the rules of logs are the exact reverse of the rules of indices.