Question

Let x₁ = 97, x₂ = `2/x_1`, x₃ = `3/x_2`, x₄ = `4/x_3`, ......, x₈ = `8/x_7` then `log_(3sqrt(2))(prod_(i = 1)^8x_i - 60)` = ______.

पर्याय

• `3/2`

• 4

• 6

• `5/2`

Answer 1

Let x₁ = 97, x₂ = `2/x_1`, x₃ = `3/x_2`, x₄ = `4/x_3`, ......, x₈ = `8/x_7` then `log_(3sqrt(2))(prod_(i = 1)^8x_i - 60)` = 4.

Explanation:

x₁ = 97, x₂ = `2/x_1`, x₃ = `3/x_2`, x₄ = `4/x_3`, ...... x₈ = `8/x_7`

⇒ `prod_(i = 1)^8x_i` = x₁.x₂.x₃.x₄.x₅.x₆.x₇.x₈

= `x_1. 2/x_1. x_3. 4/x_3.x_5. 6/x_5.x_7. 8/x_7`

= 2.4.6.8

= 384

⇒ `log_(3sqrt(2))(prod_(i = 1)^8x_i - 60)`

= `log_(18 1/2) (384 - 60)` = 2log₁₈324

= 2log₁₈18²

= 4