# Thread: Logarithm of a function

1. ## Logarithm of a function

How to take a logarithm of

$M = s(k,r)B$

2. Originally Posted by Gemini
How to take a logarithm of

$M = s(k,r)B$
what does this notation mean?

3. M is the supply of money, k is cash/deposits, r is the interest rate and B is the monetary base.

4. Originally Posted by Gemini
M is the supply of money, k is cash/deposits, r is the interest rate and B is the monetary base.
wonderful ... how are all those variables related mathematically?

5. I'm not exactly sure what you mean but I think the equation reads that the supply of money is a function of both the interest rate and k (the cash/deposit ratio) multiplied by the monetary base. I guess the RHS might as well read f(x,y)z.

6. Originally Posted by Gemini
I'm not exactly sure what you mean but I think the equation reads that the supply of money is a function of both the interest rate and k (the cash/deposit ratio) multiplied by the monetary base. I guess the RHS might as well read f(x,y)z.
why are you wanting to take the log of the "equation" ?

what, exactly, are you trying to solve?

I'm afraid I really can't help without a specific function that relates the variables and what you are trying to accomplish.

7. I found another, a much easier way to solve the problem without using logarithms but still, I'd like to know how to take a log of a function.

What I mean is that, for example, if you have Y = aX then taking a log would look like this: ln(Y) = ln(a) + ln(X).

But if it's in the form I mentioned above (i.e., M is a function of k and r), how should I write it? I'm not trying to solve anything, just to express the supply function in a logarithmic form.

8. Originally Posted by Gemini
I found another, a much easier way to solve the problem without using logarithms but still, I'd like to know how to take a log of a function.

What I mean is that, for example, if you have Y = aX then taking a log would look like this: ln(Y) = ln(a) + ln(X).

But if it's in the form I mentioned above (i.e., M is a function of k and r), how should I write it? I'm not trying to solve anything, just to express the supply function in a logarithmic form.
Until you explain what the notation $M = s(k,r)B$ means, I doubt anyone can help you.

eg. Does s(k,r) mean $k^2 + r^2$ ....? I know it doesn't but this is what we all mean when we ask you what the notations(k,r) means. We expect to get something like that as an answer.

If s(k, r) represents some multivariable function of k and r, then the best that can be done is $\ln M = \ln s(k, r) + \ln B$. If the functional form of s(k, r) is known then further progress might be possible.

9. Originally Posted by Gemini
How to take a logarithm of

$M = s(k,r)B$
$log(M)= log(s(k,r)B)= log(s(k,r))+ log(B)$