First slide

Binomial theorem for positive integral Index

Question

If the 6^th term in the expansion of ${(\frac{1}{x^{8 / 3}} + x^{2} \log_{10} x)}^{8}$ is 5600, then x equals

Moderate

A

1
B

$\log_{e} 10$
C

10
D

x does not exist

Solution

It is given that 6^th term in the expansion of ${(\frac{1}{x^{8 / 3}} + x^{2} \log_{10} x)}^{8}$ , 5600; therefore,
$\begin{array}{l} ^{8} C_{5} {(x^{2} \log_{10} x)}^{5} {(\frac{1}{x^{8 / 3}})}^{3} = 5600 {G e n e r a l t e r m T_{r + 1} = {n_{c_{r}}}^{x^{n - r}} a^{r}} \\ or 56 x^{10} {(\log_{10} x)}^{5} \frac{1}{x^{8}} = 5600 \\ or x^{2} {(\log_{10} x)}^{5} = 100 \\ or x^{2} {(\log_{10} x)}^{5} = 10^{2} {(\log_{10} 10)}^{5} \\ or x = 10 \end{array}$

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