20050710, 13:47  #1 
Jun 2005
Madison, Indiana, U.S.A.
3·7 Posts 
Exponential Digits
Can anyone tell me a way to determine how many digits are in an exponential number? For example: 1.79^308.

20050710, 13:58  #2 
Jun 2003
The Texas Hill Country
3^{2}·11^{2} Posts 
Hints:
Use logarithms The "ceiling" function will "round up" Last fiddled with by Wacky on 20050710 at 13:59 Reason: Typo 
20050710, 17:03  #3 
Jun 2004
UK
139 Posts 
y = a^x
digits in base 10 is floor(log10(y)) + 1 log10(a^x) = x*log10(a) so floor(x*log10(a)) + 1 
20050711, 02:17  #4  
Jun 2005
Madison, Indiana, U.S.A.
3×7 Posts 
Help me out here
Quote:


20050711, 03:49  #5 
Sep 2002
2·331 Posts 
Floor for positive numbers means truncate
so truncate(308*log10(1.79))+1 = truncate(77.8787)+1 = 77+1 = 78 Also using the calculator in Windows XP in Scientific mode entering 1.79 x^y 308 gives 7.5636e+77 (really more digits after the . ) so 77 digits from the exponent and 1 from the digit before the . for 78 
20050711, 16:33  #6  
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}·3^{3}·19 Posts 
Exponential digits
Quote:
How about using the natural logs (base e) I dont seem to get the same answer. Where have I gone wrong? Kindly explain step by step without programming the calculator. I get 7.5636... in a round about fashion but where does the 77 come from? Mally 

20050711, 17:31  #7  
"Bob Silverman"
Nov 2003
North of Boston
1D28_{16} Posts 
Quote:
2nd (or perhaps 3rd?) year secondary school algebra.........If you did not learn this, then there was something seriously wrong with your teacher..... Think about how to convert log_a(x) to log_b(x) where log_a denotes logarithm to the base a. 

20050711, 17:49  #8 
Bronze Medalist
Jan 2004
Mumbai,India
804_{16} Posts 
Exponential digits
Thank you R.D. (richard dermit?) That was my maths master Bro. R.D. Barrett and he was brilliant like yourself and I have a lot to thank him for Yes I have got
the answer now. I guess the 'fault lies not in the stars but in ourselves'. Thank you once again Mally 
20050712, 01:04  #9 
Jun 2005
Madison, Indiana, U.S.A.
3×7 Posts 
Thanks
I want to thank everyone who contributed to this thread. I did not have algebra in college. I suppose that whomever was efforting the class schedules did not believe that algebra was relative to electronics and computer science.

20050712, 15:02  #10 
Aug 2003
Upstate NY, USA
326_{10} Posts 
by secondary school it would be the US equivalent of high school, not college
in New York it is covered in 11th grade math (or was when I went through HS 3 years ago  they've changed the program twice since i got out) 
20050712, 16:29  #11  
Jun 2005
382_{10} Posts 
Quote:
This seems *very* condescending. You have to understand that most people left high school behind and pursued careers that had nothing to do with math, or at least not enough to care about logarithms (as useful as they are). I'd bet most people didn't remember these logarithmic identities more than a couple of months past that particular chapter in algebra class. In fact, I remember an instance when I was in high school where one of the math teachers asked me to show her how to compute logs with an arbitrary base, because she didn't remember (it's not something she normally taught). I understand you have a PhD, and you appear to be an expert in math. Understand that this means you know a *lot* more than the average Joe about these things. No need to make them feel inadequate because they happen to have enough interest to dabble a bit in your field of expertise as a hobby. They should be encouraged, not criticized. Drew Last fiddled with by drew on 20050712 at 16:38 

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