I need to get $c$ in terms of $a$.

Both $c, a\in \Bbb R^+$ $$ c^{2a} = c/a $$

I'm pretty sure that log is required to solve this, but I'm not quite sure how to approach it.

  • $\begingroup$ How about dividing by $c$ then taking the appropriate power? $\endgroup$ – Jonathan Y. Aug 29 '13 at 20:43
  • $\begingroup$ @JonathanY. Oh, that seems like it might make more sense. It just seemed to me like log would be needed, because of the powers $\endgroup$ – Alex Aug 29 '13 at 20:46

Since $c>0$, we may divide both sides by $c$ to obtain: $$ c^{2a-1} = \frac1a $$ To undo the exponent, we raise both sides of the equation to the power of $\dfrac{1}{2a-1}$ to obtain: $$ c= \left(\frac1a\right)^{\dfrac{1}{2a-1}} $$

  • 4
    $\begingroup$ It should probably be pointed out that this doesn't work if $a=\frac{1}{2}$; however, in that case the equation is $c=c/a$, so that either $a=1$ or $c=0$. $\endgroup$ – Nick Peterson Aug 29 '13 at 20:46
  • $\begingroup$ @NicholasR.Peterson If $a=\frac{1}{2}$, how can $a=1$? $\endgroup$ – Ryan Aug 29 '13 at 22:07
  • 2
    $\begingroup$ Well, it can't. So that tells you that $c=0$. :-P $\endgroup$ – Nick Peterson Aug 29 '13 at 22:08

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.