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Kai N.

asked • 12d

What is wrong in this solution?

My teacher asks us what is wrong in the following solution:

log3(x - 1)2=2

2log3(x - 1) = 2

log3(x - 1) = 1

x - 1 = 31 = 3

x = 4

1 Expert Answer

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Kai N.

I see. Thank you! Just a quick question, at which step did it go wrong? And how so?
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12d

William W.

tutor
Notice that in the initial problem you are guaranteed to have a positive argument for the logarithm because (x - 1)^2 is always positive. After you move the exponent out front making it 2log(x-1) you are no longer guaranteed to have a positive argument. That is the point that the error occurred. It should have been written 2log|x - 1|.
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11d

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