Logarithmically spacing number

Question

I would like to test several values of intensity.

I need them to be spaced logarithmically from 1 to 1000. Yet I just use 1, 10, 100, 1000, but I would like to have more data point, let`s say 10.

How could I find 10 logarithmically spaced number between 1 and 1000 in Mathematica ?

Aspirant

Answer 1

If a is start, c is end and b is number of intervals:

{a, b, c} = {1, 10, 1000};
t = (c/a)^(1/b) // N
a*t^Range[b]

1.99526
{1.99526, 3.98107, 7.94328, 15.8489, 31.6228, 63.0957, 125.893, 251.189, 501.187, 1000.}

I used N just to see better, what do we have.

Ragged

I was going to post something very similar but you beat me to it by 2 seconds. By the way, Power is Listable so you could simply do a*t^Range[b]. – Uniparous

@Heike, nice! Updated. I spotted this question from RSS 30 minutes after it was published. It's my 1st Mathematica answer, so I tried to be fast ..P – Ragged

@Ragged You could use Range[0,b] as Leonid did to get full list starting from a. – Pogy

Answer 2

Here is one way:

In[11]:= base = Block[{a}, a /. NSolve[a^9 == 1000, a][[-1, 1]]]
Out[11]= 2.15443

In[13]:= base^Range[0, 9]
Out[13]= {1., 2.15443, 4.64159, 10., 21.5443, 46.4159, 100., 
  215.443,464.159, 1000.}

EDIT

Here is a much shorter and more direct way to get the same:

In[18]:= N[10^Range[0, 3, 1/3]]

Out[18]= {1., 2.15443, 4.64159, 10., 21.5443, 46.4159, 100., 
215.443, 464.159, 1000.}

Farinose

Thank you Leonid, would you mind explaining the use of "Block", "/." & the curious "[[-1,1]]". It works, but I can`t get a grasp at that syntax yet. – Aspirant

@Aspirant I think it is much clearer just to use NSolve[a^9==1000,a,Reals]. Instead of Block one can use Formal Symbol \[FormalA] with the same success: base=\[FormalA]/.NSolve[\[FormalA]^9==1000,\[FormalA],Reals]//First. "/." is just ReplaceAll. – Pogy

@Aspirant I think, it is much easier to just use base = N[Power[1000, 1/9]]. Actually, base is a cubic root of 10. Don't know what I was thinking. – Farinose

Thank You ! I was actually looking into that. But could not find out how to get the nth roots. You answered that question to : Power & fraction ! – Aspirant

Answer 3

Solve the equation x ** 9 = 1000 -- then your numbers are: x ** 0, x ** 1, ... x ** 9.

note: where x ** y means x to the power of y

Militia