JEE PYQ: Binomial Theorem Question 38
Question 38 - 2019 (09 Apr Shift 1)
If the fourth term in the Binomial expansion of $\left(\frac{2}{x} + x^{\log_8 x}\right)^6$ ($x > 0$) is $20 \times 8^7$, then a value of $x$ is:
(1) $8^3$ (2) $8^2$ (3) 8 (4) $8^{-2}$
Show Answer
Answer: (2)
Solution
$(\log_8 x)^2 - \log_8 x - 2 = 0$, $t = 2$ or $t = -1$. $x = 8^2$ or $x = 1/8$.