SOLUTION: If a, b, and c are positive numbers such that √a/√b = 8c and ac = b what is the value of c?

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: If a, b, and c are positive numbers such that √a/√b = 8c and ac = b what is the value of c?      Log On


   

Question 1105180: If a, b, and c are positive numbers such that √a/√b = 8c and ac = b what is the value of c?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
If a, b, and c are positive numbers such that √a/√b = 8c and ac = b,
what is the value of c?
sqrt%28a%29%2Fsqrt%28b%29 = 8c
we can write it
sqrt%28a%2Fb%29 = 8c
square both sides
a%2Fb+=+64c%5E2
a = 64bc%5E2
b = a%2F%2864c%5E2%29
we know ac = b
ac = a%2F%2864c%5E2%29
divide both sides by a
c = 1%2F%2864c%5E2%29
multiply both sides by c^2
c%5E3+=+1%2F64
find the cube root of both sides
c = 1%2F4