Question

if 3 to the power of x = 4 to the power of y =12 to the power of xy , then find x+y

Answer 1

Answer:

thanks for the free points

Answer 2

Answer:

3^x = 12^xy => 3^x = 3^xy×4^xy

=> 1= 3^xy×4^xy/3^x => 1= 3^(xy-x)×4^xy ….(1)

4^y = 12^xy => 4^y = 3^xy×4^xy

=> 1 = 3^xy×4^xy/4^y => 1 = 3^xy×4^(xy-y)….(2)

From (1) and (2) we get

3^(xy-x)×4^xy = 3^xy×4^(xy-y). Since 3 and 4 are Co primes this is possible only if

xy-x = xy. and xy-y = xy => x=0 and y=0

=> x+y=0