# What is log ? What does it mean? How does it transform a number?

What is log ? What does it mean? How does it transform a number?

/I'm a code and see log being used in legacy code I have to change.

Thanks

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possible duplicate of Intuitive use of logarithms – t.b. May 9 '11 at 9:03
Have you tried Google / Wikipedia? en.wikipedia.org/wiki/Logarithm – Qiaochu Yuan May 9 '11 at 9:06
It would help to have a rough idea what the code does. In software, logs are often used for graphing or scoring for instance. – Oliver Emberton May 9 '11 at 9:29

The base-10 logarithm of a number $x$ is the power that you would need to raise 10 to to get $x$ as a result. For example, since $10^3=1000$, the base-10 logarithm of 1000 is 3.

In general the base-$b$ logarithm of $x$ (written $\log_bx$) is the number you need to raise $b$ to to get $x$. For example, if $b^y=x$ then $\log_bx=y$.

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In addition, the logarithm of a number in a given base roughly reflects one less than the number of digits the number has in that base. For example, in base 10, log 100 = 2 (=3-1 digits)

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Exponent for a number $b$ ($b$ is called base; in practice usually $10$ or $2.718\ldots =e$) to get given number. E.g. $\log_3 81 = 4$ because $3^4=81$. $\log_{10}2 = 0.30103\ldots$ because $10^{0.30103\ldots} = 2$.

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Or for a much easier explanation.... Log = # of zeroes a number (that is completely divisible by 10) has.

Example: 10000 log = 5

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You are assuming that $\log_{10} x$ is intended, which is not necessarily the case. Also, keep in mind that while $205$ has one zero, $\log_{10} 205 \neq 1$. – N. F. Taussig Sep 17 at 11:06
This question is very old and already has good answers. In my opinion, your time is much better spent contributing good answers to questions that are either (a) un-answered, or (b) very poorly answered. – TravisJ Sep 17 at 11:53