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I'm working on a software project and I need to solve for b in the following equation:

$$e^{\ln(gx)ab}-e^{\ln(x)ab}=c$$

I've tried a couple of online algebra calculators, but they cannot resolve this.

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  • $\begingroup$ Is this equivalent to $e^{\alpha b}-e^{\beta b}=c$ ? If it is, except in very few cases where this can reduce to a polynomial, consider numerical methods. $\endgroup$ – Claude Leibovici Aug 10 '18 at 10:08
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$c=e^{\ln(gx)ab}-e^{\ln(x)ab}=gx^{ab}-x^{ab}=x^{ab}(g-1)$, hence

$x^{ab}=\frac{c}{g-1}$, thus

$ab \ln (x)= \ln (c)- \ln (g-1)$.

Can you proceed ?

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  • $\begingroup$ I can solve for b with that. Let me test it... $\endgroup$ – IamIC Aug 10 '18 at 10:13

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