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$$\log_x (3-2\sqrt2)=2$$ I can't solve it, I tried everything but I can't find the solution I tried logarithmic properties but nothing works, please help!

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  • $\begingroup$ TeX: prefix the log with a backslash to make it upright: \log $\log$ vs. log $log$. $\endgroup$
    – CiaPan
    Jul 13, 2015 at 13:01
  • $\begingroup$ How about taking the square root of 3-2(surd2) that is if the equation is transformed from logarithmic to exponential. $\endgroup$ Jul 13, 2015 at 15:37

2 Answers 2

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You can simply re-write with logarithm rules: $$x^2=3-2\sqrt2$$ because $$\log_ba=c \Leftrightarrow b^c=a$$

And the answer is as simple as taking the root.

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I may banned after this comment, but technic might be helpful.

If you have had: $$ 3 + 2 \cdot \sqrt{2} $$ You would be see: $$ (\sqrt{2} + 1)^2 $$ And carefully do calculations you may provide that this statements are the same.

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