# Fractals: Problem with understanding log

Discussion in 'Homework Help' started by zulfi100, May 9, 2015.

1. ### zulfi100 Thread Starter Member

Jun 7, 2012
320
0
Hi,
I am studying fractals. It uses natuaral log. I cant understand how the author developed the second equation from the first. The first equation is:

And the second equation is:

Can some body please guide me how to obtain the second equation. I tried the following:
ln ns^D = ln (1)
ln(n) + ln(s^D) = 1
ln(n) + Dln(s) = 1
Dln(s) = -ln(n)
D = -ln(n)/ ln(s)

Zulfi.

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Last edited by a moderator: May 9, 2015
2. ### WBahn Moderator

Mar 31, 2012
18,093
4,920
What is the ln(1/s) in terms of the ln(s)?

3. ### zulfi100 Thread Starter Member

Jun 7, 2012
320
0
Hi,
Thanks for your response. I can tell you about ln(1/s). Its :
ln(1) - ln(s).
Please guide me how to obtain 2nd equation from 1st equation as i posted in #1.
Zulfi.

4. ### WBahn Moderator

Mar 31, 2012
18,093
4,920
And what is ln(1)?

5. ### zulfi100 Thread Starter Member

Jun 7, 2012
320
0
Its 1. Also tell me if the above is correct or not? If its correct then it means that if we convert ln(s) into ln(1/s) we will get a negative sign. So now we have :

ln ns^D = ln (1)
ln(n) + ln(s^D) = 1
ln(n) + Dln(s) = 1
Dln(s) = -ln(n)
D = -ln(n)/ ln(s)
D= ln(n)/ln(1/s)

Is the above correct?

Zulfi.

6. ### WBahn Moderator

Mar 31, 2012
18,093
4,920
If the ln(1) = 1, then that means that e^1 = 1. Is that correct?

What must the base, e, be raised to in order to get a result of 1?

In your work, how do you justify the following step:

ln(n) + Dln(s) = 1
Dln(s) = -ln(n)

Where did the 1 go?

7. ### zulfi100 Thread Starter Member

Jun 7, 2012
320
0
Hi,
Okay. I got my mistake.
ns^D = 1
ln(ns^D) = ln(1)
ln n + ln s^D = ln (1)
ln s^D = ln (1) - ln n
D = ( ln 1 - ln n) / ln s
D = (0 - ln n)/ln s
D= ln n / ln (1/ s)
Is this correct now???
I got the answer from google : ln (1) is actually zero.

Zulfi.

8. ### WBahn Moderator

Mar 31, 2012
18,093
4,920
That you had to Google what the ln(1) is does not bode well for you. You need to understand these fundamental concepts. Not memorize them, not be able to Google them, but to understand them.

Your work is correct now, but rather convoluted. It can be presented much more cleanly as

n·s^D = 1
ln (n·s^D) = ln(1)
ln(n) + D·ln(s) = 0
D·ln(s) = -ln(n)
D = - ln(n)/ln(s)
D = ln(n)/ln(1/s) = ln(1/n)/ln(s)

Unless (1/s) has some particularly meaning, I would probably leave it as the next to last line.