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: Convert to Exponential Form The equation \( \log_2 x = 5 \) signifies that \( x \) is the number which, when used as a logarithm with base 2, results in 5. Applying the definition of logarithms, we transform this into an exponential equation:\[x = 2^5\]Step 2: Calculate \( x \) \[x = 2^5 = 32\]Answer: The value of \( x \) is \( 32 \). The correct option is (1).