Question

Solve it.... question from bionomial theorem.​

Answer 1

In the usual (a+b)ⁿ binomial expansion the third term will be

`{n \choose 2} a^(n-2)b^2`

Note we used k=2 because the first term is k=0.

We have a=1/x, b=x^log x, n=5

5 choose 2 is (5×4)/2=10, n-2=3, so we end up with a third term of

`\displaystyle {5 \choose 2} \left(\frac 1 x\right)^(5-2)\left(x^{log_(10) x}\right)^2 = \frac{10 \,x^{2 log_(10) x}}{x^3} = 10x^{-3 + 2 \log_(10)x}`