Question

If the fourth term in the Binomial expansion of (2/x + xˡᵒᵍ₈ ˣ)⁶ (x > 0) is 20 × 8⁷, then a value of x is:
(A) 8³
(B) 8⁻²
(C) 8 (D) 8²

Answer 1

Answer:

your answer is (D):8²

Step-by-step explanation:

1.) The fourth term of the binomial expansion is: 20×(8/x³)×(xˡᵒᵍ₈ ˣ)³=20×8^7

2.) By further solving this equation

You got x³ˡᵒᵍ₈ ˣ×x^(-3)=8^6

3.) Now taking log both the side of base 8

i.e. (3ˡᵒᵍ₈ ˣ-3)ˡᵒᵍ₈ ˣ=6ˡᵒᵍ₈ 8

4.) Then you got an quadratic equation

i.e. 3(ˡᵒᵍ₈ ˣ)² - 3(ˡᵒᵍ₈ ˣ) - 6 = 0.

5.) Now let (ˡᵒᵍ₈ ˣ)=t

6.) You got 3t² - 3t - 6=0

7.) By solving this you get two

values of t i.e. t=1 or t=2

8.) Now put your value in forth binomial term and compare it

which given in step 1.

9.) Now by putting and comparing you get only one value that is satisfies the equation which is given in step 1.

10.) After that comparison you got x=8².