What does logarithm and anti-logarithm mean?

Answer 1

A logarithm is an exponant. For example 100 = 10^2

100 equals 10 to the 2nd power. So 2 (the exponant) is the log of 100. The log of 1000 would be 3.

The anti-log means you start with the exponant and go backwards to get a regular number. So the anti-log of 3 is 1000.

Adding logs is the same as multplying regular numbers.

100 * 1000 = 100,000;
2 + 3 = 5 & the anti log of 5 is 10,000.

Note. the exponant of 2 is only equivalent to 100 if 10 is being rasied to the 2nd power. The number being raised to a power is called the base. Base 10 is the default, but other bases are possible.

E.g. 25 = 5^2 so log (base 5) of 25 is also 2.

Now you will probably never use base 5, but you may use base 2.7183 which is called 'e'. Weird huh? e is called the natural log (aka LN or e^x) because it shows up in a lot of natural processes, like how fast things cool.

So pretty simple right?
Turn a number into an exponant that's taking the log.
Turn an exponant into a number that's taking the anti log.

Finding the log of 100 or 1000 is easy, but if, for example, you want to know the log of 500 is 2.7, you'll need to use the calculator.

One more tiny oddity. Any number raised to the 0th power is one. So regardless of base the log of 1 is zero, and the antil log of 0 is 1. This ties into the fact that adding logs is the same as multiplying numbers. Adding zero doesn't change a number, nor does multiplying by 1

Have fun.

Answer 2

Logarithm Means

Answer 3

Logarithms are used in medicine for HIV viral load counts. the log of the data transforms the data to a normal distribution.
most statistical tests can be then be performed on normally distributed data.

Answer 4

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