Question

If x, y, and z are integers greater than 1, and (327)(510)(z) = (58)(914)(xy), then what is the value of x? (1) y is prime (2) x is prime

Answer 1

1) 5

2) 5

Explanation:

Data provided in the question:

(3²⁷)(5¹⁰)(z) = (5⁸)(9¹⁴)(
`x^y`)

Now,

on simplifying the above equation

⇒ (3²⁷)(5¹⁰)(z) = (5⁸)((3²)¹⁴)(
`x^y`)

or

⇒ (3²⁷)(5¹⁰)(z) = (5⁸)(3²⁸)(
`x^y`)

or

⇒
`((3^(27))/(3^(28)))((5^(10))/(5^8))z=x^y`

or

⇒
`((5^2)/(3))z=x^y`

or

⇒
`(5^2)/(3)=(x^y)/(z)`

we can say

x = 5, y = 2 and, z = 3

Now,

(1) y is prime

since, 2 is a prime number,

we can have

x = 5

2) x is prime

since 5 is also a prime number

therefore,

x = 5