Coefficient Party

Probability Level 3

(x83+x2 log10x)8 \left ( x^{- \frac 8 3} +x^2 \ \log_{10}x \right )^8

For what value of xx 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 (a+b)^n is (n0)an,(n1)an1b,(n2)an2b2,{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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