Question

Which of the following inequality is true for \( x>0 \)?

• A. \( \log(1 + x)<\frac{x}{1+x} \)
• B. \( x<\log(1+x) \)
• C. \( \frac{x}{1+x}<\log(1+x) \)
• D. \( \frac{x}{1+x}<\log(1+x)<x \)

Hint:

Inequalities involving logarithms can be checked using properties such as \( \log(1 + x)>x \) for \( x>0 \).

Answer 1

The Correct Option is B

We apply logarithmic properties to verify that the inequality holds for \( x>0 \).