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# Intro to logarithm properties (1 of 2)

Sal introduces the logarithm identities for addition and subtraction of logarithms. Created by Sal Khan.

## Want to join the conversation?

• What is the real life use for Logarirhims? Why would people need them?
• The pH scale and the Richter scale are both logarithmic and in chemistry there are occasions that we need them to find a percent of disagreement in values. They can also be used in the growth count of a culture of microbes.
• Why is this piece of math method called logarithm?
• Actually, it doesn't seem to be a contraction of "logical arithmetic". The Online Etymology Dictionary says (http://etymonline.com/index.php?term=logarithm&allowed_in_frame=0) "literally "ratio-number," from Greek logos "proportion, ratio, word" (see logos) + arithmos "number" (see arithmetic)". Wikipedia says (https://en.wikipedia.org/wiki/Logarithm) "Napier [...] introduced the word "logarithm" to mean a number that indicates a ratio: λόγος (logos) meaning proportion, and ἀριθμός (arithmos) meaning number".
• What happens if another number is added to the equation?

If you don't know what I mean, here is an example:

log2 A + log2 B + 3

Note that 2 is the base.
• That expression could be simplified to
log₂(AB) + 3
But note that 3 = log₂(2³), so we can substitute that:
log₂(AB) + 3 = log₂(AB) + log₂(2³)
= log₂(AB) + log₂(8)
= log₂(8AB)

So, the general rule would be:

logₐ (b) + c
= logₐ ( baᶜ )
• Is it possible to have negative logarithms when dealing with properties. Let's just say log^2 -35 or something similar where you can expand it?
• Yes, the logarithms that have negative numbers as their argument are called complex logarithms, However it would be hard to handle them because their values can vary.

http://en.wikipedia.org/wiki/Complex_logarithm
• So, logarithmic addition is a process of exponential multiplication?
• Yes, because like solving problems that don't represent exponential properties, things can be simplified.
• Why did you put 81 as 1/81 instead of 81/1 if we started with 81 as a whole number?
• He did that because multiplying 1/9 *1/81 is the same as 1/9 divided by 81. Multiplying by 1/81 is easier to work out than 1/9 divided by 81. Always remember: dividing by a number is the same as multiplying it by it's inverse.
Example:
10/2 is the same a 10*1/2=5
20/4 is the same as 20*1/4=5
If you want to multiply instead of divide, just take the inverse or reciprocal of the number you want to divide by.
• Why can we assumed log1 as log base10 of 1?
• Because when there is no base specified that's an automatic 10.
This is what we call a common logarithm
That's why......
log 1 = log (base 10) 1

Note: A common logarithm is a logarithm with a base 10 so that's....
log (base 10) R=P or simply written as log R=P
where:
R= is the resulting number after raising a base to a certain power.
P= power
• why is the quality so bad
• Video created on Nov 16, 2007.

So yea, I think the quality is normal for a video created that long time ago.