SOLUTION: Given 2^m × (1/8)^n = 128 and 4^m ÷ 2^(-4n) = 1/6, find the value of (m-n).

Algebra ->  Test -> SOLUTION: Given 2^m × (1/8)^n = 128 and 4^m ÷ 2^(-4n) = 1/6, find the value of (m-n).       Log On


   

Question 1144759: Given 2^m × (1/8)^n = 128 and 4^m ÷ 2^(-4n) = 1/6, find the value of (m-n).
Found 2 solutions by Edwin McCravy, MathTherapy:
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
system%282%5Em%2A%281%2F8%29%5En+=+128%2C+4%5Em%2F2%5E%28-4n%29+=+1%2F6%29

system%28+2%5Em%2A%288%5E%28-1%29%29%5En+=+2%5E7%2C+4%5Em%2A2%5E%284n%29+=+1%2F6%29

system%282%5Em%2A8%5E%28-n%29+=+2%5E7%2C+%282%5E2%29%5Em%2A2%5E%284n%29+=+1%2F6%29

system%282%5Em%2A%282%5E3%29%5E%28-n%29+=+2%5E7%2C+2%5E%282m%29%2A2%5E%284n%29+=+1%2F6%29

system%282%5Em%2A2%5E%28-3n%29+=+2%5E7%2C+2%5E%282m%2B4n%29+=+1%2F6%29

system%282%5E%28m-3n%29+=+2%5E7%2C+2%5E%282m%2B4n%29+=+1%2F6%29

system%28m-3n+=+7%2C+2%5E%282m%2B4n%29+=+1%2F6%29

system%28m=3n%2B7%2C+2%5E%282m%2B4n%29+=+1%2F6%29

By substitution:

2%5E%282%283n%2B7%29%2B4n%29+=+1%2F6

2%5E%2810n%2B14%29+=+1%2F6

Multiply both sides by 2

2%2A2%5E%2810n%2B14%29+=+2%2Aexpr%281%2F6%29

2%5E%2810n%2B14%2B1%29+=+1%2F3

2%5E%2810n%2B15%29+=+3%5E%28-1%29

Take natural logs of both sides:

ln%282%5E%2810n%2B15%29%29+=+ln%283%5E%28-1%29%29

%2810n%2B15%29ln%282%29+=+-ln%283%29

Divide both sides by ln(2)

10n%2B15=-ln%283%29%2Fln%282%29

10n=-15-ln%283%29%2Fln%282%29

Multiply both sides by 1/10

n=expr%281%2F10%29%28-15-ln%283%29%2Fln%282%29%29

m=3n%2B7

m=expr%283%2F10%29%28-15-ln%283%29%2Fln%282%29%29%2B7

But you don't want m or n, you want m-n



m-n=expr%282%2F10%29%28-15-ln%283%29%2Fln%282%29%29%2B7

m-n=expr%281%2F5%29%28-15-ln%283%29%2Fln%282%29%29%2B7

Edwin

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Given 2^m × (1/8)^n = 128 and 4^m ÷ 2^(-4n) = 1/6, find the value of (m-n). 
I believe you did post this after: test/1144760: Given 2^m × (1/8)^n = 128 and 4^m ÷ 2^(-4n) = 1/16, find the value of (m-n).

If I'm correct, why didn't you DELETE the former?

Why did you allow someone to solve the original problem: "test/1144759," when it contained an error, as itw's SUPPOSED to be: 

, instead of: ?

BTW,