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

Answer:

1) 5

2) 5

Step-by-step 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

⇒ $(\frac{3^{27}}{3^{28}})(\frac{5^{10}}{5^8})z=x^y$

or

⇒$(\frac{5^2}{3})z=x^y$

or

⇒$\frac{5^2}{3}=\frac{x^y}{z}$

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