# Difference between log and ln

• Dominic M Sangma

#### Dominic M Sangma

What is the difference between log and ln??

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Log is based on powers of 10, often called Common Log. Ln is based on powers of e (that's 2.71828...), called Natural Log.

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Tom

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Log is based on powers of 10
That depends on the context.
In physics it is typically base 10, in mathematics it is usually base e, and in computer science it is base 2.

If you want to make the base clear, use lg (10), ln (e) or ld (2).

fresh_42
I think ##\log = \ln## became more and more the standard, and ##\ln## is a bit old fashioned. A clear line or convention cannot be drawn as it depends on the author what he uses. If no base is mentioned, I'll always vote for base ##\mathbf{e}##, even in CS, because they vary only by a constant factor which usually doesn't play a role, e.g. in runtime calculations.

The base matters if you want to determine e.g. how many bits you need to represent something in binary.

The base matters if you want to determine e.g. how many bits you need to represent something in binary.
Yeah, all O(1) to me.

I must admit it's a bit of a Bill Gates attitude: "I don't care the hardware."

jbriggs444