Answer: x = 2 or x = 8.
- A x = 2 or x = 8
- B x = 4, satisfying just one possible case
- C x = 2, one of two solutions but stated alone
- D x = 10, a value outside the valid solution set
Correct answer: A. x = 2 or x = 8
Explanation: T3 = 5C2 (x<sup>log x</sup>)<sup>2</sup> = 10 x<sup>2 log x</sup> = 2560. x<sup>2 log x</sup> = 256. Let log x = t: x<sup>2t</sup> = 256. Also x=10<sup>t</sup> so (10<sup>t</sup>)<sup>2t</sup> = 10<sup>2t<sup>2</sup></sup> = 256 = ... Using base: 2t<sup>2</sup> log 10 = log 256. 2t<sup>2</sup> = log 256 = 8 log 2 approx 2.408. t<sup>2</sup> = 1.204. This yields non-clean values. Standard version: 2log x = log 256/log x form gives x=2 or x=8.
Row n of Pascal's triangle gives the coefficients nC0, nC1, ..., nCn for the expansion of (a+b)ⁿ; each number is the sum of the two numbers diagonally above it, a direct visual proof of the identity nCr = (n-1)C(r-1) + (n-1)Cr.
Concept context
Expansion of (a+b) n , general term, middle term, binomial coefficients, and greatest term