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?
:
{{{log(a,(b)) = 3/2}}} and {{{log(c,(d))= 5/4}}}
write the exponent equiv
:
b = {{{a^(3/2)}}}  and  d = {{{c^(5/4)}}}
solve for a and c
a = {{{b^(2/3)}}}  and c = {{{d^(4/5)}}}
given that
a - c = 9
Substitute for a and c
{{{b^(2/3)}}} - {{{d^(4/5)}}} = 9
:
{{{b^(2/3)}}} = {{{d^(4/5)}}} + 9
b = {{{(d^(4/5)+ 9)^(3/2)}}}
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 = {{{(125^(2/3))}}} = 25
Find c
c = {{{(32^(4/5))}}} = 16
a - c = 9