# Different ways that Log appears

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

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Hootenanny
Staff Emeritus
Gold Member
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?
Correct, loge(x) is identical to ln(x) and is given the name "natural logarithm".
However my table of integrals has e^x. Is this the same too?
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.

tiny-tim
Homework Helper
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?
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.
However my table of integrals has e^x. Is this the same too?