Logarithmic ProblemDate: Wed, 22 Feb 95 20:29:39 -800 From: Stan Olson Can you help me solve this? log 3^X = 6 + (1/2)log 9^x Thanks Date: Wed, 22 Feb 1995 22:08:49 -0500 (EST) From: Dr. Ken Subject: Re: logarithm equation Hello there! Well, to solve this equation, you'll have to remember a couple of properties of logarithms. Namely, Log(x^y) = y*Log(x) Log(xy) = Log(x) + Log(y). To solve this equation, we can simplify the left side of the equation to get Log(3^x) = x*Log(3). Similarly, on the right side, we get (1/2)Log(9^x) = (1/2)Log(3^2x) = Log((3^2x)^1/2) = Log(3^x) = x*Log(3) So our equation is x*Log(3) = 6 + x*Log(3). Subtracting x*Log(3) from both sides, we can see that this equation has no solutions in the real numbers. Thanks for the question! -Ken "Dr." Math |
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