Solve the equation (9^log x)^2 = 81^(log y)

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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.

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