Question

if 2352 = 2 to power x × 3 to power y × 7 to power z , then the value of x +y + z is

Answer 1

According to the question, we have

2352 = 2 to power x × 3 to power y × 7 to power z

Or

2352 = 2^x + 3^y + 7^z  .............. (1)

The prime factorization of  2352 gives us

2352 = 2 × 2 × 2 × 2 × 3 × 7 × 7

2353 = 2^4 + 3^1 + 7^2    ............. (2)

Comparing (1) and (2) , we have

2^x + 3^y + 7^z  = 2^4 + 3^1 + 7^2

So we have  

x = 4 , y = 1 , z = 2

so we have

x + y + z = 4 + 1 + 2

x + y + z = 7