Questions: What happens to the value of f(x)=log4 x as x approaches 0 from the right? f(x) approaches negative infinity

Solution Steps

• The logarithmic function \( \log_{4} x \) is defined for \( x > 0 \).
• As \( x \) approaches 0 from the right (\( x \to 0^+ \)), \( \log_{4} x \) tends to negative infinity because the logarithm of a very small positive number is a large negative number.

• As \( x \) approaches infinity (\( x \to +\infty \)), \( \log_{4} x \) tends to positive infinity because the logarithm of a very large number is a large positive number.

• The options provided are:
  1. \( f(x) \) approaches negative infinity
  2. \( f(x) \) approaches 0
  3. \( f(x) \) approaches infinity
• From Step 2, we know that \( f(x) \) approaches infinity as \( x \to +\infty \), so the correct option is \( f(x) \) approaches infinity.

Final Answer