Exponential Issues – 5/26/03 Classic
x and y are positive integers 5^x-5^y=2^(y-1)5^(x-1) , what is the value of xy?
(A) 48
(B) 36
(C) 24
(D) 18
(E) 12


Answer E

(5^x-5^y)/5^(x-1)=2^(x-1)

5-5^(y-x+1)=2^(y-1)

5=2^(y-1)+5^(y-x+1)

y-x+1=0 for 5=2^(y-1)+5^(y-x+1)

and 2^(y-1)=4 ==> y=3 and x=4

xy=12

answer E

how come

y-x+1=0 is assumed?

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