Thread: Solving for x in an exponential equation

Hello, one question has proved ​ insurmountable to me. Here it is:
(3/4)^x =(27/64)^(2x-3)

Here is what I have tried:



(3)^x/(4)^x=(27)^(2x-3)/(64)^(2x-3)

Then i cross multiplied to get...

(192)^(2x^2-3x)=(108)^(2x^2-3x)

I know that I need to make the bases the same, but i can't see how to do that at this point. Some guidance would be greatly appreciated.

Originally Posted by takaj

Hello, one question has proved ​ insurmountable to me. Here it is:
(3/4)^x =(27/64)^(2x-3)

Originally Posted by Plato

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Originally Posted by takaj

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The point is if then .

I showed how the bases are the same.

Thank you. I got it now.