To solve the equation \( 2^x = 16 \), we need to determine the value of \( x \) that makes this equation true. Let's break this down step-by-step. ### Step 1: Understand the Equation The equation \( 2^x = 16 \) means that \( 2 \) raised to the power of \( x \) equals \( 16 \). Our goal is to find the exponent \( x \). ### Step 2: Express 16 as a Power of 2 To solve for \( x \), it helps to express \( 16 \) as a power of \( 2 \). We can do this by recognizing that: \[ 16 = 2^4 \] This means that \( 16 \) can be rewritten in terms of base \( 2 \). ### Step 3: Set the Exponents Equal Now that we have both sides of the equation in terms of base \( 2 \), we can rewrite the original equation: \[ 2^x = 2^4 \] Since the bases are the same (both are \( 2 \)), we can set the exponents equal to each other: \[ x = 4 \] ### Conclusion Thus, the value of \( x \) is \( 4 \). Therefore, the correct option is: **C. 4** ### Explanation of Other Options - **A. 2**: This option suggests that \( 2^2 = 4 \), which is not equal to \( 16 \). Therefore, this option is incorrect. - **B. 3**: This option suggests that \( 2^3 = 8 \), which is also not equal to \( 16 \). Hence, this option is incorrect. - **D. 5**: This option suggests that \( 2^5 = 32 \), which is greater than \( 16 \). Therefore, this option is incorrect. ### Common Pitfalls - **Misunderstanding Exponents**: A common mistake is to confuse the values of exponents. Remember that \( 2^2 = 4 \) and \( 2^3 = 8 \) are much smaller than \( 16 \). - **Not Recognizing Powers**: Sometimes, students may not recognize that \( 16 \) can be expressed as \( 2^4 \). Familiarity with powers of \( 2 \) can help avoid this mistake. ### Revision Summary - To solve \( 2^x = 16 \), express \( 16 \) as a power of \( 2 \) (i.e., \( 16 = 2^4 \)). - Set the exponents equal: \( x = 4 \). - The correct answer is \( C. 4 \). - Always check if the bases are the same when dealing with exponential equations.