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Basic Question 4 of 7
Is this statement true or false?
On a logarithmic scale, the space between 100 and 10 is 10 times the space between 1 and 10.
User Contributed Comments 8
| User | Comment |
|---|---|
| surob | WHY? |
| Janey | 1/10=.1, 10/100=.1, 100/1000=.1 |
| surob | Still, didn't understand. Can someone explain in more detail? Thanks |
| dave79 | basically, logarithmic scale is always a normal distribution and here it contradicts by saying diff spacing between 100 and 10 and 1 and 10 |
| rufi | think this like this 10, 10^1, 10^2....10^n...there is difference of 1 in exponential value |
| stratus | Because 1, 10, 100, etc are all multiplied by the factor 10. An important property of logarithms is log(A*B)=log(A) + log(B). So if you take any number X, the logarithm is log(X). If you take the number 10*X, the logarithm is log(10)+log(X). Therefore, in LOGARITHM space, every time you multiply by 10, you are ADDING log(10) to where you previously were. So going from 1, 10, 100, 1000, etc, you are just shifting over log(10) each time. |
| aakash1108 | thanks @ stratus.....very useful. |
| cfaajay | log 1 = 0 log 10 = 1 log 100 = 2 log 1000 = 3 and so on... |
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Learning Outcome Statements
explain the relationship between normal and lognormal distributions and why the lognormal distribution is used to model asset prices when using continuously compounded asset returns
CFA® 2025 Level I Curriculum, Volume 1, Module 6.