Logb(base a)=3/2

log d(base c)=5/7
and a-c=9
then b-d=?
Plz help me

1 answer

Hmmm.

b = a^(3/2)
d = c^(5/7)

a = b^(2/3)
c = d^(7/5)

a-c=9, so

b^(2/3) - d^(7/5) = 9

I assume we want integer solutions, so let's list the squares of cube roots and the 7th powers of 5th roots:

n n^(2/3)
1 1
8 4
27 9
64 16
125 25
216 36

n n^(7/5)
1 1
32 128
243 2187
1024 4096

I'm not getting any joy here. Any other ideas?
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