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How can I solve:

$$(a^{n-5/2}-b^{n-5/2})=c$$

for $n$? $a$, $b$ and $c$ are known constant.

It seems that Solve cannot solve it and Reduce goes on forever and never produces an output.

a=1/6, b=0.0057 c=15952.6

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  • $\begingroup$ What's known about a,b,c? $\endgroup$ – Ulrich Neumann Aug 8 at 12:32
  • $\begingroup$ @UlrichNeumann I have edited the post to add the values of the constants. $\endgroup$ – mattiav27 Aug 8 at 12:35
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    $\begingroup$ There is no analytical solution to this question in general. It is of the form $A^n - B^n = C$. Need to solve it numerically. $\endgroup$ – Nasser Aug 8 at 12:58
  • $\begingroup$ Try Plot[lhs-rhs,{n,...}] your equation and you'll see there is no solution with given values of constants. $\endgroup$ – Alx Aug 9 at 4:25
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NMinimize doesn't find a solution for your equation:

a = 1/6
b = 0.0057
c = 15952.6
NMinimize[{(a^(n - 5/2) - b^ (n - 5/2) - c)^2}, n]
(*{2.54474*10^8, {n -> 2.81377}}*) 
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