Question

If x and y satisfy simultaneously the equations (2x)log2 = (3y)log3 and 3logx = 2logy then the value
of (x-1 + y), is 4.​

Answer 1

Answer:

If ( x , y )  is the answer of the given equation  ( 2 x ) log 2 = ( 3 y ) log 3  and  3 log x = 2 log y  then x is equal to?

Explanation:

Taking the logarithm on both sides (the first equation) we get

log ( 2 ) ( log ( 2 ) + log ( x ) ) = log ( 3 ) ( log ( 3 ) + log ( y ) )

Doing the same with the second equation:

log ( y ) = log ( x ) ⋅ log ( 3 )/ log ( 2 )

Substituting

a = log ( x )

we get

log ( x ) log 2 ( 2 ) − log 2 ( 3 )/ log ( 2 ) = − ( log 2 ( 2 ) − log 2 ( 3 ) )  

so  

a = − log ( 2 )

log ( x ) = log ( $2^{-1}$)

x = 1 /2

In the first equation we get

1 = 3 y

y = 1 /3

Answer 2

False, ans. 5

1/3 +1/2 = x+y

1/x+1/y=2+3=5