I've been asked to solve th
I've been asked to solve this and I've tried a few things but I have trouble eliminating . I first tried taking the natural log:
I don't know what to do from here so I decided to try another method:
And then I get stuck here, I'm all out of ideas. My guess is I've overlooked something simple…
Answer & Explanation
Your equation has two obvious solutions which are and . The last solution is not rational () and cannot be obtained using simple functions. You cannot get the last root using logarithms.
There is a special function, that is the inverse of when the latter is restricted to . Using this, expressions of the form can be solved as . You want to find the solution(s) to the equation . Rewrite as and raise each side to the power of . We then arrive at
Multiple both sides by to arrive at
Apply to both sides to get
Multiply through to find
Which is equal to 2.