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This means that the value of the LHS and RHS are equal. I take this to mean that "5 raised to some exponent is equal to both x and ##\frac{2x+3}{2x-3}##.

I can now write this as ##x=\frac{2x+3}{2x-3}## because since the function is one-to-one, one output corresponds to exactly one input (the input being the argument).

But what if the case was reversed? That is, the bases were different and the arguments were equal? Could I equate the bases to each other? It would be like saying that two different numbers, raised to some exponent, are equal to the same thing.