CFA Practice Question

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CFA Practice Question

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.
Correct Answer: False

1, 10, 100, and 1,000 are equally spaced on a logarithmic scale.

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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