Bill_Graham
New member
- Joined
- Jul 28, 2020
- Messages
- 1
I have a math problem I don't know how to approach. Seems similar to one that I could find answered on the internet, where you have (2^x)(3^y)(5^z), and the question was how many combinations of factors will this possibly produce, the answer was (x + 1)(y + 1)(z + 1), and which makes sense. NOW I have been given a more difficult challenge. Here is the problem I must solve, and I don't know how to do it clean and neat and without the help of a calculator. (I am not allowed to use a calculator.) So here goes:
Given that we have an exponential expression (2^x)(3^y)(5^z).
Limiting the product of the exponential expression to a number between 5,000 and 6,000.
And, we will look for a sum of digits of the exponents, x, y, and z, such that x + y + z = either "5" or "8" or "11" or "18"... any one of these.
I won't bore you with my convoluted thinking on this matter. And, yes, I know, I can probably take a couple of days of time to grind though this and learn from the experience, but I still would not learn the generalized solution that I am sure someone has already learned and can share with me here. I have never run into a problem quite like this. I don't see a practical application, but it is probably a good thing to know, I suppose. So if anyone can answer this question with a nice neat generalized methodology, not involving the use of calculators (just maybe some scratch paper and some simple/clever math that way), maybe also they could point out to me the skill I am supposed to learn from knowing how to solve such a problem.
Thanks, and I can't wait to see what it is I have not thought of. (Maybe the "skill" I need is to be able to take square roots of such numbers as 5,000 or 6,000 or anything in between right out of my head? Just a thought.)
Given that we have an exponential expression (2^x)(3^y)(5^z).
Limiting the product of the exponential expression to a number between 5,000 and 6,000.
And, we will look for a sum of digits of the exponents, x, y, and z, such that x + y + z = either "5" or "8" or "11" or "18"... any one of these.
I won't bore you with my convoluted thinking on this matter. And, yes, I know, I can probably take a couple of days of time to grind though this and learn from the experience, but I still would not learn the generalized solution that I am sure someone has already learned and can share with me here. I have never run into a problem quite like this. I don't see a practical application, but it is probably a good thing to know, I suppose. So if anyone can answer this question with a nice neat generalized methodology, not involving the use of calculators (just maybe some scratch paper and some simple/clever math that way), maybe also they could point out to me the skill I am supposed to learn from knowing how to solve such a problem.
Thanks, and I can't wait to see what it is I have not thought of. (Maybe the "skill" I need is to be able to take square roots of such numbers as 5,000 or 6,000 or anything in between right out of my head? Just a thought.)