#3**+5 **

This is best seen by examining some simple numbers. For example:

There are 3 digits in 10^2 (= 100). 2*log(10) = 2 add 1 to get 3.

There are 4 digits in 20^3 (= 8000). 3*log(20) = 3.903... Take integer part and add 1 to get 4

There are 7 digits in 35^4 (= 1500625). 4*log(35) = 6.176... Take the integer part and add 1 to get 7

etc.

.

Alan
May 2, 2015

#1**+5 **

1). Take log to the base 10 of the number log(2014^2022) = 2022*log(2014)

$${\mathtt{2\,022}}{\mathtt{\,\times\,}}{log}_{10}\left({\mathtt{2\,014}}\right) = {\mathtt{6\,680.808\: \!240\: \!691\: \!985\: \!784\: \!6}}$$

2) Take the integer part (6680) and add 1 to get 6681. That's how many digits there are.

.

Alan
May 1, 2015

#2**0 **

Really Alan ?? :/:/

Would you like to talk about this a bit please -it is really weird :/

Melody
May 2, 2015

#3**+5 **

Best Answer

This is best seen by examining some simple numbers. For example:

There are 3 digits in 10^2 (= 100). 2*log(10) = 2 add 1 to get 3.

There are 4 digits in 20^3 (= 8000). 3*log(20) = 3.903... Take integer part and add 1 to get 4

There are 7 digits in 35^4 (= 1500625). 4*log(35) = 6.176... Take the integer part and add 1 to get 7

etc.

.

Alan
May 2, 2015