Logarithmic Differentiation

Taking log₅ on both sides
$(16(%5Clog_5x)%5E3%20-68(%5Clog_5x))(%5Clog_5x)%20%3D%20-16$
Let ( log₅x)=t
16t⁴ - 68t² + 16 = 0
4t⁴ + 16t² - t²+4=0
(4t² - 1)(t²-4) = 0
$t%3D%C2%B1%5Cfrac%7B1%7D%7B2%7D%5C%20or%20%C2%B12$
So log₅x = $%C2%B1%5Cfrac%7B1%7D%7B2%7D%5C%20or%20%C2%B12$
$%E2%87%92%20x%3D5%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%20%2C%205%5E%7B-%5Cfrac%7B1%7D%7B2%7D%7D%20%2C%205%5E2%2C%205%5E%7B-2%7D$
$%5Ctherefore$ Product = $(5)%5E%7B%5Cfrac%7B1%7D%7B2%7D-%5Cfrac%7B1%7D%7B2%7D%20%2B2-2%7D$
$%3D%205%5E0%20%3D%201$

So, the correct answer is 1.

High-Yield Trend

Chapter Questions
2 MCQs

Official Solution

Official Solution

Logarithmic Differentiation

High-Yield Trend

Chapter Questions 2 MCQs

Official Solution

Official Solution

Chapter Questions
2 MCQs