Question

(1000^n/3) +(2000^m/4) +(7000^r/7) =10^4, thenn+m+r=​

Answer 1

Answer:

n + m + r = 14

Step-by-step explanation:

(1000^n/3) +(2000^m/4) +(7000^r/7) =10^4

1000^(n/3) = 1000^(n/3)

2000^(m/4) = 1000^(m/4) * 2^(m/4)

7000^(r/7) = 1000^(r/7) * 7^(r/7)

1000^(n/3) + 1000^(m/4) * 2^(m/4) + 1000^(r/7) * 7^(r/7) = 10^4

To have one possible Solution

1000^(n/3) = 1000^(m/4) = 1000^(r/7)

1000^(n/3) (1 + 2^(m/4) + 7^(r/7) ) = 10^4

1000  = 10^3

10^n (1 + 2^(m/4) + 7^(r/7) ) = 10^3 * 10

1000^n = 10^3   & 1 + 2^(m/4) + 7^(r/7) = 10

=> n = 3  , m = 4  & r = 7 is the solution

n + m + r = 3 + 4 + 7 = 14

n + m + r = 14