Re: number of digits in n^p

• To: mathgroup at smc.vnet.net
• Subject: [mg60463] Re: [mg60415] number of digits in n^p
• From: "Ingolf Dahl" <ingolf.dahl at telia.com>
• Date: Sat, 17 Sep 2005 02:31:45 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Not extremely difficult!

The function (Floor[Log[10, x]] + 1) gives the number of digits (before the
decimal point) of a positive number.

Use the logarithm laws to obtain

digitsofpower[n_Integer /; n > 0, p_Integer /; p >= 0] :=
Floor[p*Log[10,n]]+ 1

E.g.

digitsofpower[67, 89]

returns 163

Best regards

Ingolf Dahl
Sweden

-----Original Message-----
From: George [mailto:orangepi77 at yahoo.com]
To: mathgroup at smc.vnet.net
Subject: [mg60463] [mg60415] number of digits in n^p

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

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