Question

The value of the integral \( \int_{2}^{4} \left( \frac{\log t}{t} \right) \, dt \) is equal to:

• A. \( \frac{1}{2}(\log 2)^2 \)
• B. \( \frac{5}{2}(\log 2)^2 \)
• C. \( \frac{3}{2}(\log 2)^2 \)
• D. \( (\log 2)^2 \)
• E. \( \frac{3}{2}(\log 2) \)

Hint:

Using properties of logarithms like $\log(a^n) = n\log a$ before or during evaluation makes handling the limits much simpler.

Answer 1

The Correct Option is C