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Old 2005-07-10, 13:47   #1
ndpowell
 
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Question Exponential Digits

Can anyone tell me a way to determine how many digits are in an exponential number? For example: 1.79^308.
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Old 2005-07-10, 13:58   #2
Wacky
 
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Hints:

Use logarithms

The "ceiling" function will "round up"

Last fiddled with by Wacky on 2005-07-10 at 13:59 Reason: Typo
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Old 2005-07-10, 17:03   #3
marc
 
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y = a^x

digits in base 10 is floor(log10(y)) + 1

log10(a^x) = x*log10(a) so floor(x*log10(a)) + 1
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Old 2005-07-11, 02:17   #4
ndpowell
 
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Question Help me out here

Quote:
Originally Posted by marc
y = a^x

digits in base 10 is floor(log10(y)) + 1

log10(a^x) = x*log10(a) so floor(x*log10(a)) + 1
OK! I am lost on the terms "floor" and "ceiling" beyond their obvious meanings. Where do I plug in my numbers? I tried it on a hand calculator. No luck.
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Old 2005-07-11, 03:49   #5
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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
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Old 2005-07-11, 16:33   #6
mfgoode
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Question Exponential digits

Quote:
Originally Posted by dsouza123
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
Fair enough!
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
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Old 2005-07-11, 17:31   #7
R.D. Silverman
 
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Quote:
Originally Posted by mfgoode
Fair enough!
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
Converting from one logarithm base to another is something one learns in
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.
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Old 2005-07-11, 17:49   #8
mfgoode
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Lightbulb 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
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Old 2005-07-12, 01:04   #9
ndpowell
 
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Smile 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.
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Old 2005-07-12, 15:02   #10
tom11784
 
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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)
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Old 2005-07-12, 16:29   #11
drew
 
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Quote:
Originally Posted by R.D. Silverman
2nd (or perhaps 3rd?) year secondary school algebra.........If you did not
learn this, then there was something seriously wrong with your teacher.....
Hey R.D. Silverman,

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 2005-07-12 at 16:38
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