I need some help on two log questions. I do understand everything of the problem until the final answer, it does not make sense.(adsbygoogle = window.adsbygoogle || []).push({});

Problem 1:

log_{3}(x-1)^2 - log_{3}(x^2 -1) = -1 + log_{3}(x-1)

2log_{3}(x-1) - log_{3}(x^2 -1) = -1 + log_{3}(x-1)

2log_{3}(x-1) - log_{3}(x-1) - log_{3}(x^2 -1) = -1

log_{3}(x-1) - log_{3}(x^2 -1) = -1

log_{3}x-1/(x-1)(x+1) = -1

log_{3}1/x+1 = -1

=3^-1 = 1/3

x = 2 <=== why does it equal two?

Problem 2:

logx^5 + log x = (log x)(2logx)

5logx + logx = 2(logx)^2

6logx = 2(logx)^2

3 = logx <=== why does it equal 3? How does it turn from 6logx to 3?

x = 10^3

Thank you!

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# Question on logs

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