Solve the exponential equation 2^x = 16.

To solve the equation (2^x = 16), we first express 16 as a power of 2. We know that (16) can be rewritten as (2^4), since (2^4 = 2 \times 2 \times 2 \times 2 = 16).

Now, we have the equation:

[ 2^x = 2^4 ]

Since the bases are the same (both are base 2), we can equate the exponents:

[ x = 4 ]

This indicates that when (x) equals 4, (2^x) equals 16. Therefore, the correct answer is 4.

To clarify the reasoning for why the other choices aren’t correct:

• Choosing 2 would suggest that (2^2 = 4), which is not equal to 16.
• Choosing 3 would imply (2^3 = 8), which still does not match 16.
• Choosing 5 leads to (2^5 = 32), which exceeds 16.

Thus, the only value that satisfies the equation (2^x = 16) is (