Question

If \( \log_2 x = 5 \), what is the value of \( x \)?

• A. \( x = 32 \)
• B. \( x = 25 \)
• C. \( x = 20 \)
• D. \( x = 16 \)

Hint:

Remember: The equation \( \log_b a = c \) is equivalent to \( a = b^c \), where \( b \) is the base of the logarithm.

Answer 1

The Correct Option is A

Step 1: Rewrite the logarithmic equation in exponential form The logarithmic equation \( \log_2 x = 5 \) means that \( x \) is the number whose logarithm base 2 equals 5. By the definition of logarithms, we can convert this into an exponential equation: \[ x = 2^5 \] Step 2: Solve for \( x \) \[ x = 2^5 = 32 \] Answer: Therefore, the value of \( x \) is \( 32 \). So, the correct answer is option (1).