Can anyone explain what log() is and in this equation what does log actually do to get the answer? Please show the equation expanded with log replaced by whatever it did in full steps. Will give fg if I understand.

log((1071.80/500)/log(1+0.1)
=8.00005

So in a book it appears like this


I kind of understand what log does now after reading a few more explanations, but still need someone to help me expand this equation to show what log did.

This post was edited by JukeBOXX on Sep 19 2013 07:13am

Log() is the equivalence to natural logarithm, it gives you back the natural base to e.

Edit: sorry, was writing this before seeing your edit. Will look into how to explain though.

If your question is, what log() does, is lg(x) / lg(e)

For a question about the divison:
log( u : v ) = log(u) - log(v)

This post was edited by Onimo on Sep 19 2013 07:20am

Wait, don't we assume base 10 for log? And ln is natural logarithm? :S

Either way, it's irrelevant in this problem if you keep things consistent, since your expression is equivalent to

(log(1071.8)-log(500))/log(1.01) = log base 1.01 of 1071.8 - log base 1.01 of 500, so a change of base happens anyway.



log(a) = b, this means that 10^b = a (because logs are base 10)

so if you were wondering 10 to the what power gives you a, you would take the log of a

LOG PROPERTIES

log(a)/log(c) = log base c of a

log base c of a = b, this means that c^b = a

log(x*y) = log(x) + log(y) (can be used to derive the below properties)

log(x^z) = log(x*x*x*x z times) = z * log(x)

log(x/y) = log(x * 1/y) = log(x) + log(1/y) = log(x) + log(y^-1) = log(x) + -1*log(y) (what Onimo posted)


Edit:

btw, if you wanna know why log(x*y) = log(x)+log(y)

log(x)+log(y) = z

10^(log x + log y) = 10^z
10^log(x) * 10^log(y) = 10^z
x*y = 10^z now log both sides
log(x*y) = z

This post was edited by zackill4 on Sep 19 2013 09:03am

The question is compound interest.


In my book -



On the website where I found the formula it has -



I'm pretty sure that my i = their k.

So the answer is N, and I need to find that.
FV=1071.80
PV=500
K=10%
N=
I=



So



Using log it gives me the correct answer of 8, but I'm still not understanding how it got that. I am studying accounting, I'm not sure it is supposed to have something as complicated as log being used. It is not mentioned in my book anywhere and there is no example formula given for this question, the questions all have had two parts (until this question) A+B, A = use formula, B = use financial calculator, but for every single other question there has been an example formula to use to get the answer because we are supposed to know how to and show working out. Is there a way to do this without log, if not how would you work this out on a piece of paper with no calculator? Please use the red text and set it out how you would on paper.

Ok, so for this specific problem

we have 500 * (1+.1)^years = 1071.80

this is because your money grows by 10% each year, so you gain .1*money
therefore your total money after interest is money + .1*money, or 1.1*money

each year this grows, so 1.1*1.1*1.1... for years times


ok now log both sides and you get log(1.1^years) = log(1071.8/500)

now by the properties i listed, you know that this is years * log(1.1) = log(1071.8/500)

years = log(1071/500)/log(1.1)


Next time please post the whole question so we don't waste time guessing what you want to know...

This post was edited by zackill4 on Sep 19 2013 09:18am

Sorry.

I want to know how to do it without using log or if it is even possible to do it without using log

Why would you want to solve this problem without logs? You could take the initial expression and guess the years until it comes out right, but what you're saying doesn't make sense. If you want to solve it algebraically, you need logs. If you still don't understand logs, read my first post more carefully where I pretty much detail everything about them.

As someone who is studying accounting and will be constantly working with exponents (for interest), you better get used to logs now


Edit
The reason you need logs is to solve this part
(1.1^years) =1071.8/500

How do you know what exponent will make this expression true? This must be solved with logs, or guess and check/graphically using software

This post was edited by zackill4 on Sep 19 2013 09:28am

I was talking about the method Math.log() in programming languages, which takes base e.

Spent like 3hours trying to figure this out, maybe more. Turns out you are right I do have to do guess and check by putting it in a table and then use a formula.


This is a different question but of the same type.
Note: FVIV10 = (1 + i)^n = (1+0.1)^n
The 3 you choose yourself because it is between the exceeding and preceding numbers FVIV





The answer this gives is 11.51, but the question deals with annual compound interest, annual being the keyword so really the answer is 12, you aren't getting any interest till the end of that year. The answer in the book is 11.52, tiny discrepancy of 0.01 but yeh... I am not sure why the answer isn't 12 in the book, guess maybe they will specify in detail if they want an answer like 11.51 or a whole year like 12. Silly

This post was edited by JukeBOXX on Sep 19 2013 12:01pm

Duh, thats what the solver function is for