Find the solution of 3^{4x} = 9^{(x-1)/2}.
First, recognise that 3^2 = 9. Recall the rule for multiplying indices, that (a^b)^c = a^{bc}. Then, substitute 3^2 in place of 9 to get 3^{4x} = (3^2)^{(x-1)/2}. Use the rule for multiplying indices, so that the equation is now 3^{4x} = 3^{x-1}. This implies 4x=x-1, and therefore 3x = -1, and finally, x = -1/3 is the solution.
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