# Thread: logarithm and exponential calculus

1. ## logarithm and exponential calculus

So I missed out a couple of weeks on maths and missed out quite a bit
I don't understand what is this "In" thing in the questions. I only have formulas with either "log" and "x", "d", "v" signs.
https://prnt.sc/hjyiz4
image1 (1).JPG
These questions are the ones I'm stuck on. I don't need all of them done, I just need someone to use one of the examples and explain it? The words in blue are the answers. pls help if you can

2. ## Re: logarithm and exponential calculus

ln is natural log, i.e. it has a base of e instead of 10 like log.

For differentiating you have ln(f(x)) so the derivative is f'(x)/f(x).

For integrating you want to divide by the derivative of the power. Note for 4a that isn't possible as it has lnx rather than a form of x e.g. 4x so consider indice laws. A good thing to note is that e^lnx = x and ln(e^x) as they are the inverse of each other.

NOTE: 2lnx = ln(x^2) but I'm assuming you know your log laws

3. ## Re: logarithm and exponential calculus

Originally Posted by otakuworld
So I missed out a couple of weeks on maths and missed out quite a bit
I don't understand what is this "In" thing in the questions. I only have formulas with either "log" and "x", "d", "v" signs.
https://prnt.sc/hjyiz4
image1 (1).JPG
These questions are the ones I'm stuck on. I don't need all of them done, I just need someone to use one of the examples and explain it? The words in blue are the answers. pls help if you can
woah this isn't something you should do when you've just started learning it.

But anyways in 4a) you need to know your indices and log law well.

$\int e^{2-lnx} \ dx = \ \ \int \ e^2 e^{-lnx} \ \ dx = \\ \\ e^2 \int e^{ln\frac{1}{x}} \ \ dx \\ \\ = e^2 \int \frac{1}{x} \ \ dx \\ \\ = e^2 ln(x) + C$

P.S holy crap you posted this at 4:10 am?!!

4. ## Re: logarithm and exponential calculus

thank you! and I didn't realise you could see the time I was up...shhh..ಠ_ಠ

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