Given , find the value of .
Working with logarithm is tricky, we try to transform the question to an exponential question.
Then, we have
Here comes the critical observation:
Observe that .
Divide throughout by , we get .
Solving using quadratic formula (and reject the negative value since and has to be positive for their logarithm to exist),
We get .
If you have any questions, please feel free to ask me by posting a comment, or emailing me.
(I will usually explain in much more detail if I teach in person, than when I type the solution)