Question

If x, y, and z are positive integers and 2^x * 3^y * 5^z = 54,000, what is the value of x + y + z

Answer 1

Given:

If x, y, and z are positive integers, then

`2^x* 3^y* 5^z=54000`

To find:

The value of
`x+y+z`.

Solution:

First we need to find the prime factors of 54000.

`54000=2* 2* 2* 2* 3* 3* 3* 5* 5* 5`

`54000=2^4* 3^3* 5^3` ...(i)

We have,

`54000=2^x* 3^y* 5^z` ...(ii)

On comparing (i) and (ii), we get
`x=4,y=3,z=3`.

The sum of
`x,y,z` is:

`x+y+z=4+3+3`

`x+y+z=10`

Therefore, the value of
`x+y+z` is 10.