I have seen this question for bc, but how do you do this in dc? For example, if the command were q, I would want to use it like this:
10k
5q2q/
To compute log_2(5).
There's no built-in command for this in dc, but you can implement any of the numerical methods for computing a logarithm as macros.
For example, this one computes ln(x) using ln((1+y)/(1-y)) Taylor series expansion:
# L (x -- y)
# Natural logarithm of `x`.
[ 1-d2+/
d2*Sk # Initialize multiplier
d*Sy # Initialize multiplier factor
0Ss # Initialize accumulator
10K^Sp # Initialize 10^k power
[ d1r/lk*ls+lsrdss # Update accumulator
-lp*d*1 [s_q]s_>_ # Check precision
lkly*sk 2+ # Update multiplier and counter
lfx
]Sf
1lfxLs
LkLyLpLfs_s_s_s_] sL
Use it like this:
10k
5lLx 2lLx /p
It's not optimal, in particular for large numbers (x ≫ 1), but a method with a faster convergence can also be implemented this way, if needed.
Squeezed version (somewhat faster):
[1-d2+/d2*Skd*Sy0Ss10K^Sp[d1r/lk*ls+lsrdss-lp*d*1[s_q]s_>_lkly*sk2+lfx]Sf1lfxLsLkLyLpLfs_s_s_s_]sL