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Re: number of digits in n^p

• To: mathgroup at smc.vnet.net
• Subject: [mg60491] Re: number of digits in n^p
• From: Bill Rowe <readnewsciv at earthlink.net>
• Date: Sun, 18 Sep 2005 01:15:47 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

On 9/16/05 at 3:48 AM, orangepi77 at yahoo.com (George) wrote:

>i wonder if there is a formula, a function, or a method in
>mathematica to know the number of digits in  n raised to the power
>of p without calculating the result, such as 67^89 will give us a
>number with 163 digits in it, is there a way to know this result
>without actually calculating 67^89 thanks George

I think what you are looking for is

Ceiling[n Log[10,p]] or using your particular case

In[3]:=Ceiling[89*Log[10, 67]]

Out[3]=163
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