David Troyer

2021-12-29

What is the difference between log and ln?

I was told that its

I was told that its

David Clayton

Beginner2021-12-30Added 36 answers

Usually $\mathrm{log}\left(x\right)$ means the base 10 logarithm; it can, also be written as ${\mathrm{log}}_{10}\left(x\right)$ .

${\mathrm{log}}_{10}\left(x\right)$ tells you what power you must raise 10 to obtain the number x.

$10}^{x$ is its inverse.

$\mathrm{ln}\left(x\right)$ means the base e logarithm; it can, also be written as ${\mathrm{log}}_{e}\left(x\right)$

$\mathrm{ln}\left(x\right)$ tells you what power you must raise e to obtain the number x.

$e}^{x$ is its inverse.

chumants6g

Beginner2021-12-31Added 33 answers

When you specify the base you should always use

When

The base is

At some previous point, the author explicitly set that “all logs should be understood as base b”,

From the context, the base, if not e , is clear - and it will usually be 2, or, less often, 10.

It doesn’t matter. For instance, if the statement is that a function is

Vasquez

Expert2022-01-08Added 669 answers

Yes, big difference.

Log is used for base ten. You’ve probably seen an equation like this:

If you know y how do you find x?

You take the Log of the equation

So

Ln is the natural log. The natural log is used to solve for a when you know b in the following equation:

to solve for a when you know y, take the natural log of

So

So how does Ln y compare to

Let

Then

Hope this helps

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