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

Question

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

anonymous · Answer

@mathslover @.Sam.

anonymous · Answer

Is it 125 ?

kc_kennylau · Answer

Yes

phi · Answer

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

phi · Answer

* $$ 10^{120} \cdot 10^3 \cdot 11 $$

phi · Answer

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

ganeshie8 · Answer

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