Solve the equations for ` x and y:(3x)^(log3)=(4y)^(log 4), 4 ^(log x) = 3 ^(log y)`.

Explanation

`(3x)^(log3)=(4y)^(log 4), 4 ^(log x) = 3 ^(log y)`
` rArr (log 3) (log 3x) = (log 4)(log 4y)`
` and (log x)(log 4) = (log y)(log 3)`
` rArr (log 3)(log 3+ log x) = (log 4) (log 4+ log y)`
` and (log x ) (log 4) = ( log y ) (log 3)`
` rArr (log 3)(log 3+ p) = (log 4)(log 4+q)`
`and p(log 4) = q(log 3) ` (where p log x and q = log y)
` rArr (log 3)(log3+(qlog3)/(log4))=log 4(log 4+ q)`
(eliminating p)
` rArr (log 3)^(2)- (log 4) ^(2) = ((log 4)^(2) - (log 3)^(2))/(log 4) q`
` rArr q =-log 4`
` rArr log y = log 4^(-1)`
` rArr y= 1//4`
Now,` p(log 4) = q (log 3)`
` or p (log 4)=-(log 4)(log 3)`
` or p =- log 3`
` or log x = log 3^(-1)`
` or x = 1//3`