SOLUTION: I had this exponent problem. 3^x-2 = 81 --> 3^4 = 81 I can solve it by trial and error (evaluating values for x)to get the exponent. But I figure that there has to be a bett

Algebra ->  Exponents -> SOLUTION: I had this exponent problem. 3^x-2 = 81 --> 3^4 = 81 I can solve it by trial and error (evaluating values for x)to get the exponent. But I figure that there has to be a bett      Log On


   

Question 460410: I had this exponent problem.
3^x-2 = 81 --> 3^4 = 81
I can solve it by trial and error (evaluating values for x)to get the exponent. But I figure that there has to be a better way to find the root. Any help you can provide would be greatly appreciated because I have similar problems to solve of this kind.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
3%5E%28x-2%29+=+81+=+3%5E4
==> x - 2 = 4 ==> x = 6.
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1) You said you can solve for x by trial-and-error, but in fact you have never produced any value for x. So you still don't know how "to solve" the equation.
2) I don't know what "comprehensive" way you're looking for when what you're doing is basically reducing both terms so that they have the same bases, and then equating powers. Sorry that didn't seem obvious to you.
3) Just repost the problem so that other tutors can explain to you every word of the solution, as well as show you the "comprehensive" way that's eluded you so far.