Solve the exponential equation 2^x = 16.

Solve the exponential equation 2^x = 16.

• A. 2
• B. 3
• C. 4
• D. 5

Answer: (C)

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 \(

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 (