SOLUTION: Let a, b, c, d be positive integers such that loga(b)=3/2 and logc(d) =5/4. If a − c = 9, then b − d equals?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Let a, b, c, d be positive integers such that loga(b)=3/2 and logc(d) =5/4. If a − c = 9, then b − d equals?      Log On


   

Question 877245: Let a, b, c, d be positive integers such that loga(b)=3/2 and logc(d) =5/4. If a − c = 9, then b − d equals?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Let a, b, c, d be positive integers such that loga(b)=3/2 and logc(d) = 5/4.
If a − c = 9, then b − d equals?
:
log%28a%2C%28b%29%29+=+3%2F2 and log%28c%2C%28d%29%29=+5%2F4
write the exponent equiv
:
b = a%5E%283%2F2%29 and d = c%5E%285%2F4%29
solve for a and c
a = b%5E%282%2F3%29 and c = d%5E%284%2F5%29
given that
a - c = 9
Substitute for a and c
b%5E%282%2F3%29 - d%5E%284%2F5%29 = 9
:
b%5E%282%2F3%29 = d%5E%284%2F5%29 + 9
b = %28d%5E%284%2F5%29%2B+9%29%5E%283%2F2%29
Plotting this equation on my Ti83, got integer solutions of
b = 125, d = 32
Find b - d
125 - 32 = 93
:
:
Check this
Find a
a = %28125%5E%282%2F3%29%29 = 25
Find c
c = %2832%5E%284%2F5%29%29 = 16
a - c = 9