# Homework Help: Different ways that Log appears

1. Mar 12, 2008

### grscott_2000

Not so much a question query here but a query about how my question is written.

Im having to do some integration and my question has one part loge (log sub e). I think that this is just natural log which i usually see written as ln(x). Is this correct? However my table of integrals has e^x. Is this the same too? I seem to be getting confused by all the different ways of writting these logrithms. Can someone clarify please as to what each of these terms really means?

Regards

2. Mar 12, 2008

### Hootenanny

Staff Emeritus
Correct, loge(x) is identical to ln(x) and is given the name "natural logarithm".
However, ex is not the same as the natural logarithm, it is in fact it's inverse. Explicitly,

$$\log_e\left(e^x\right) = \ln\left(e^x\right) = x$$

And,

$$e^{\ln(x)} = x$$

Similarly,

$$\log_a\left(a^x\right) = x$$

And,

$$a^{\log_a(x)} = x$$

I hope this helps clear things up for you.

3. Mar 12, 2008

### tiny-tim

Hi!

$$log_e(x)$$ means the same as ln(x).

You would pronounce it "logarithm, base e".

I suspect that the examiner is worried that some people use "log" for natural logs (I prefer that), and some for log-base-10, so he's written "$$log_e(x)$$" to remove any doubt.
Sorry, I don't follow this part of your query.

4. Mar 12, 2008

### grscott_2000

Many thanx..... Thats just what I was looking for. Things should be straightforward now, well as straightforward as integration can be i suppose!

Again many thanx for the help