Question

Find the number of digits in 2^120x125x88x5^120 .
It is rather difficult

Answer 1

@mathslover @.Sam.

Answer 2

Is it 125 ?

Answer 3

Yes

Answer 4

I would do this
\[ 2^{120}\cdot 125 \cdot 88 \cdot 5^{120} \]
notice that we can write this as
\[ 2^{120}\cdot 5^{120} \cdot 5^3 \cdot 2^3 \cdot 11 \\
(2\cdot 5)^{120} \cdot (5 \cdot 2)^3 \cdot 11 \\
2^{120} \cdot 10^3 \cdot 11
\]

Answer 5

* \[ 10^{120} \cdot 10^3 \cdot 11 \]

Answer 6

or
\[ 11 \cdot 10^{123} \]

to figure out how many digits that is, look for a pattern
\( 11 \cdot 10^1\) = 110 or 3 digits
\( 11 \cdot 10^2\) = 1100 or 4 digits
the rule appears to be
\( 11 \cdot 10^n\) has 2+n digits

Answer 7

a dumb way is to
http://www.wolframalpha.com/input/?i=log%282%5E120x125x88x5%5E120+%29&a=*FunClash.log-_*Log10-