To solve the equation \( 2^x = 32 \), we need to determine the value of \( x \). Let's break this down step-by-step. ### Step 1: Understand the Equation The equation \( 2^x = 32 \) means that we are looking for a power \( x \) such that when 2 is raised to that power, the result is 32. ### Step 2: Express 32 as a Power of 2 To solve for \( x \), it helps to express 32 as a power of 2. We can do this by repeatedly dividing 32 by 2: - \( 32 \div 2 = 16 \) - \( 16 \div 2 = 8 \) - \( 8 \div 2 = 4 \) - \( 4 \div 2 = 2 \) - \( 2 \div 2 = 1 \) Counting the divisions, we see that we divided by 2 a total of 5 times. Therefore, we can express 32 as: \[ 32 = 2^5 \] ### Step 3: Set the Exponents Equal Now that we have expressed 32 as \( 2^5 \), we can rewrite the original equation: \[ 2^x = 2^5 \] Since the bases (2) are the same, we can set the exponents equal to each other: \[ x = 5 \] ### Conclusion Thus, the value of \( x \) is 5. Therefore, the correct option is **B**. ### Explanation of Other Options - **Option A (4)**: If \( x = 4 \), then \( 2^4 = 16 \), which is not equal to 32. Therefore, this option is incorrect. - **Option C (6)**: If \( x = 6 \), then \( 2^6 = 64 \), which is also not equal to 32. Hence, this option is incorrect. - **Option D (3)**: If \( x = 3 \), then \( 2^3 = 8 \), which again is not equal to 32. Thus, this option is incorrect. ### Summary of Key Points - To solve \( 2^x = 32 \), express 32 as a power of 2. - Recognize that \( 32 = 2^5 \). - Set the exponents equal: \( x = 5 \). - The correct answer is **B**. ### Revision Summary - Understand how to express numbers as powers of their base. - Use the property of exponents to equate powers when bases are the same. - Check each option by substituting back into the original equation to verify correctness. - Practice similar problems to reinforce the concept of solving exponential equations.