I am trying to solve a problem with the following form

$$e^{\displaystyle A\log(x)}$$

$e^{\log(x)}$ is simply $x$, but how do I go about separating the $A$?


1 Answer 1


Use one of the rules for logarithms to move the $A$. In particular, the rule you want is $A\log x = \log(x^A)$.

  • $\begingroup$ So is it just x^a? $\endgroup$ Feb 5, 2014 at 0:18
  • $\begingroup$ Yes it is just $x^A$. $\endgroup$ Feb 5, 2014 at 0:19
  • $\begingroup$ You can also (not coincidentally) use the laws of exponentials to do this; namely, $e^{ab}=(e^a)^b$. So, you can write $e^{A\log x}=(e^{\log x})^A=x^A$. $\endgroup$ Feb 5, 2014 at 0:33

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