Given 2^x = 3^y =6

Taking log on all the sides we get

Log 2^x = Log 3^y = Log6

xLog2 = yLog3 = Log 6

x= Log6/Log2

y= Log6/Log3

We know that Log(ab) = Log a + Log b

therefore Log6 = Log 2 + Log 3

x+y = (Log 6/ Log 2) + (Log 6/Log 3) = Log 6*((Log 2 + Log 3)/Log 2 Log 3) = (Log 6*Log 6/ Log 2* Log 3) = xy

**x+y = xy**