Question

If the $6^{th}$ term in the expansion of ${[\frac{1}{x^{8/3}}+x^{2}lo{g}_{10}x]}^8$ is 5600 , then $x$ =

• A. 10
• B. 8
• C. 11
• D. 9

Answer 1

The correct option is A 10

From given, we have,

6th term ${=}^8{C}_5{x}^{-\frac{8}{3}\times 3}(x^2\log x{)}^5$

$\Rightarrow \frac{8\times 7\times 6}{3\times 2}\times x^{-8}\times x^{10}(\log x{)}^5=5600$

$x^2({\log }_{10}x{)}^5=100$

$\therefore x=10$