Well, let's learn one more thing...
Please show your work.
You obviously know a logarithm is needed, so I'll give you this step.
Now what?
Could somebody please help a middle aged student who hasn't done any 'proper' maths for 25 years (and is starting to remember why he preferred English lessons) with this problem where I need to express with as the subject? I have the answer but mine doesn't match it
Many thanks
By definition, a logarithm is the inverse of an exponential. So logarithms undo exponentials and exponentials undo logarithms.
In other words:
If then where is any base.
Proof:
(since logarithms undo exponentials).
Similarly:
If then where is any base.
Proof:
(since exponentials undo logarithms).
Now, looking at your question.
.
In this case our base is the number , Euler's Number. It pops up so often that you should research it...
We want to undo the exponential, so we use a logarithm of base .
since the logarithm undoes the exponential
.
Note: Since the logarithm of base occurs so often in nature, it is called the Natural Logarithm, and is often denoted as .
So it may be that the answer is written as
.
Ah now I see. So
It's so bloomin obvious, why didn't I see that.
This was the last of a list of exercises and that whole thing threw me and made it seem more complicated than it really was, when all I had to do was bring down the whole exponent and multiply by one.
Thanks very much Niall and prove it. Now I can finally get to bed.