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Given:

$$\ln(xa)= b\ln(c-x)$$

I am unsure of how to manipulate the values within the natural logs to solve for x while the factor b remains. I can safely move in circles by applying the definition of the logarithm to yield the exponential form.

$$ax = (c-x)^{b}$$

Is there a way to make forward progress? I know all values ($a$, $b$, $c$, $x$) to be real and $b$ to be a positive integer. I am only interested in real solutions.

  • 0
    $\ln(a*b)=\ln a+\ln b$ is definitively handy here.2012-02-18
  • 0
    Can you do this special case: $x = (1-x)^{10}$. If you cannot do that, there is not much hope for the general one.2012-02-18

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