SOLUTION: Given 2^m × (1/8)^n = 128 and 4^m ÷ 2^(-4n) = 1/16, find the value of (m-n).

Algebra ->  Test -> SOLUTION: Given 2^m × (1/8)^n = 128 and 4^m ÷ 2^(-4n) = 1/16, find the value of (m-n).       Log On


   

Question 1144760: Given 2^m × (1/8)^n = 128 and 4^m ÷ 2^(-4n) = 1/16, find the value of (m-n).
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


2%5Em+%2A+%281%2F8%29%5En+=+128
2%5Em+%2A+%282%5E-3%29%5En+=+2%5E7
2%5E%28m-3n%29+=+2%5E7
m-3n+=+7 [1]

4%5Em+%2F+2%5E%28-4n%29+=+1%2F16
%282%5E2%29%5Em+%2F+2%5E%28-4n%29+=+2%5E%28-4%29
2%5E%282m%29+%2A+2%5E%284n%29+=+2%5E%28-4%29
2%5E%282m%2B4n%29+=+2%5E-4
2m%2B4n+=+-4 [2]

[1] and [2] are a pair of linear equations in m and n. Solve the pair of equations by your favorite method and evaluate (m-n).