Question

when you multiply it all out, how many digits are in the answer to 2^350 x 3^3 x 5^351

Answer 1

There are floor(log(2^350*3^3*5^351))+1 digits
Which is floor(350*log(2) + 3*log(3) + 351*log(5))+1 digits
= floor(352.13033..)+1 digits
= 353 digits.

The floor function rounds the number down to the nearest integer.

Answer 2

log is log base 10 for this question.

Answer 3

wow really?

Answer 4

what?

Answer 5

that is cool. i would have done something more prosaic and said
\[2^{350}\times 5^{351}=2^{350}\times 5^{350}\times 2=10^{350}\times 2\]\]

Answer 6

and
\[2\times 3^3=54\]

Answer 7

@mathboy that is quite nice.
but i think i am getting a different answer or am i confused?

Answer 8

The 3rd 2 in your equation should be a 5 i think, if that makes any difference..

Answer 9

(and the 4th)

Answer 10

ooh it should be
\[5\times 3^3=135\] got it

Answer 11

so it would be 135 digits?

Answer 12

hmm am i still off by one?

Answer 13

oh not not 135 digits

Answer 14

it is
\[135\times 10^{350}\] which has 353 digits

Answer 15

hhhmmm:

http://openstudy.com/groups/mathematics#/groups/mathematics/updates/4e657bce0b8b1f45b4b4b2fb

Answer 16

someone else said 352 digits.

Answer 17

Yep i think that's correct.

Answer 18

10^1 has 2 digits though right, so 10^x has x+1 digits.

Answer 19

that some else who said 352 digits on another copy of this question was me - and I was off by one digit .

353 digits is correct - wolfram confirms it:

http://www.wolframalpha.com/input/?i=2^350+x+3^3+x+5^351