Number system question


#1

If 73 base x is equal to 54 in base y system,them what can be the possible values of x and y?


#2

X=3 AND Y=4
(73)x=(54)y
7x+3=5y+4
7x-5y=4-3
7x-5y=1
x=3,y=4
so 73 base 3 and 54 base 4.


#3

Any value of x and y satisfying following equations :
7x - 5y = 1 and
x > 7 and
y > 5


#4

Its not correct since 73 base x, will definitely have number/digits from (0,1,2...x-1),
that means according to your answer i.e. base 3 for 73 contradicts as 3(base) < 7(digit used).