# How can I solve this equation for the exponent n?

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

• What's known about a,b,c? – Ulrich Neumann Aug 8 at 12:32
• @UlrichNeumann I have edited the post to add the values of the constants. – mattiav27 Aug 8 at 12:35
• 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. – Nasser Aug 8 at 12:58
• Try Plot[lhs-rhs,{n,...}] your equation and you'll see there is no solution with given values of constants. – Alx Aug 9 at 4:25

NMinimize doesn't find a solution for your equation:
a = 1/6