Solve the equation (9^log x)^2 = 81^(log y)
The equation `(9^log x)^2 = 81^(log y)` has to be solved.
It should be noted that the equation has two variables x and y. As a result it is not possible to find a unique solution. Only an expression for one of the variables in terms of the other can be determined.
`(9^log x)^2 = 81^(log y)`
=> `9^(2*log x) = (9^2)^(log y)`
=> `9^(2*log x) = 9^(2*log y)`
As the base is the same, the exponent can be equated.
=> `2*log x = 2*log y`
=> `x = y`
The relation between x and y derived from the given equation is y = x.