Log to what base?

edorajh · 2003-12-17, 11:43

What is the base of logarithms in this formula?:

(e^gamma/log 2) * log log x

(Formula for the number of Mersenne primes less than or equal to x)

GP2 · 2003-12-17, 15:13

I believe it's natural log (base "e").

edorajh · 2003-12-17, 15:45

All three logs?

GP2 · 2003-12-17, 16:06

Yes, I think the "log 2" means the log of 2, not log of something to the base 2.

Usually when mathematicians refer to log, they mean natural log.

edorajh · 2003-12-17, 16:27

Thanks.

I was thinking that ln is simbol for natural log.

nfortino · 2003-12-17, 16:31

Quote:

Originally posted by edorajh
All three logs?

Looking at the justification at http://www.utm.edu/research/primes/.../heuristic.html I get e^gammalog_elog₂x/log_e2. However, assuming x is large (which needs to be true for other assumptions in the argument as well), taking the inner log to be the natural log makes almost no difference, so it is said that all three logs are base "e."

2003-12-17, 11:43	#1
edorajh Oct 2003 Croatia 2³·3·19 Posts	Log to what base? What is the base of logarithms in this formula?: (e^gamma/log 2) * log log x (Formula for the number of Mersenne primes less than or equal to x)

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2003-12-17, 15:13	#2
GP2 Sep 2003 5·11·47 Posts	I believe it's natural log (base "e").

2003-12-17, 15:45	#3
edorajh Oct 2003 Croatia 111001000₂ Posts	All three logs?

2003-12-17, 16:06	#4
GP2 Sep 2003 5·11·47 Posts	Yes, I think the "log 2" means the log of 2, not log of something to the base 2. Usually when mathematicians refer to log, they mean natural log.

2003-12-17, 16:27	#5
edorajh Oct 2003 Croatia 2³×3×19 Posts	Thanks. I was thinking that ln is simbol for natural log.