I am so sorry. You guys must just be sick of me by now.
I have two equations I can't figure out how to solve.
\(\displaystyle \sqrt{\ln x} = \ln \sqrt{x}\)
I started off squaring both sides:
\(\displaystyle \ln x = \frac{1}{4}(\ln x)(\ln x)\)
Then dividing by 1/4 and one of the logs from the right:
\(\displaystyle 4 = \ln x\)
\(\displaystyle e^4 = x\)
Which is one of the answers, the other being 1. Where did the one come from?
And the second, I'm not really even sure what to do.
\(\displaystyle (\log_{3} x)^2 - \log_{3} x^2 = 3\)
I keep ending up with:
\(\displaystyle 27x^2 = x^{\log_{3} x}\)
And from there I'm stuck.
Thanks for any help.