Question

For the relation (2x) base9=(3y) base 7, the possible values of x and y are

Answer 1

"(43) base x=(34)base y

(43) base x in decimal=(4*x +3*x^0)base 10 =4x+3

Similarly,

(34)base y in decimal=(3*y +4*y^0)base10

=3y+4

According To question, 4x+3=3y+4

i.e 4x-3y=1

x= (1+3y)/4

The largest digit in both the no is 4 so the base of the number must be greater than 4.

so,x>4

(1+3y)/4>4

1+3y>16

3y>15

y>5

so y>5 i.e y>=6

Also since x>4 so x>=5

Keep in mind that x and y are natural numbers.

x=(3y+1)/4 and y=(4x-1)/3

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