Reputation: 35275

How to calculate the log of a number using bc?

I want to calculate the log (base 10) of a number. How can I do this using bc?

Upvotes: 70

Answers (8)

Ray Toal

Reputation: 88398

Invoke bc with the -l option (to enable the math library) like so:

$ echo 'l(100)/l(10)' | bc -l
2.00000000000000000000

Use the l function which is the natural log. Take the natural log of the number you are interested in then divide it by the natural log of 10.

Upvotes: 100

LeoR

Reputation: 716

Since bc -l only gives you the natural logarithm you can define the log function quickly yourself:

define log(x) { return l(x)/l(10) }
log(10)
1.0000000

Upvotes: 0

hyperkinetic

Reputation: 21

As many others have pointed out, bc invoked with the -l option will include the standard math libraries, and offer their functionality through extensions. @dee pointed to additional extensions that solved the problem I had of calculating log2() that led me to this post. I've found no way to "install" them, but they can be loaded at runtime by including the file when invoking bc:

bc -l extensions.bc

If you want to make this the default behavior, define the environment variable BC_ENV_ARGS to -l /pathToExtension/extensions.bc in your shell's profile or .rc

Upvotes: 1

Tilo

Reputation: 33732

the logarithm of x in respect to base b can be computed given any logarithm function to an arbitrary base k -- that's actually pretty cool!

log_b(x) = log_k(x) / log_k(b)

e.g.

log_b(x) = ln(x) / ln(b)

if b=10:

log_10(x) = ln(x) / ln(10)

and -l in bc enables the math library

so that's why this works:

# bc -l
l(100) / l(10)
2.00000000000000000000

Upvotes: 54

Palash Kanti Kundu

Reputation: 372

bc does not directly gives the logarithm in other than except or in other ways, using bc, we can calculate only ln(x). So, to get any other base logarithm, it is wise to remember some identities. The basic one is -

log base 10 (x) = log base e (x) / log base e (10)

Here I am giving you some examples of different base logarithms -

totan@Home-Computer ~ $ bc -l
bc 1.06.95
Copyright 1991-1994, 1997, 1998, 2000, 2004, 2006 Free Software Foundation, Inc.
This is free software with ABSOLUTELY NO WARRANTY.
For details type `warranty'. 

l(8)/l(2)
3.00000000000000000002

l(1000)/l(10)
3.00000000000000000000

l(100000)/l(100)
2.50000000000000000000

l(100000)/l(10)
5.00000000000000000001

l(81)/l(3)
4.00000000000000000001

l(64)/l(4)
3.00000000000000000000

quit()
totan@Home-Computer ~ $

Hope this helps you.

Upvotes: 2

dee

Reputation: 19

Poster specifically requested log 10.

I have bc 1.06.95 on Ubuntu 12.10. "l(x)" in this version of BC is not base 10. It is natural log (base e). This is confirmed here and BC has worked this way since some time:

http://linux.about.com/od/commands/l/blcmdl1_bc.htm

I suspect what you need to make log base 10 work is the BC extension:

http://x-bc.sourceforge.net/extensions_bc.html

Not sure correct way to install this, and got errors trying to post it here.

Dominic-Luc Webb

Upvotes: 1