Coefficient Party

$\left ( x^{- \frac 8 3} +x^2 \ \log_{10}x \right )^8$

For what value of $$x$$ is the sixth term in the binomial expansion above equal to 5600?

Details and Assumptions

• The first few term of the binomial expansion $$(a+b)^n$$ is $${n \choose 0} a^n, {n \choose 1} a^{n-1} b, {n \choose 2} a^{n-2} b^2, \ldots$$
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