College Math Placement Practice Test 2025 - Free College Math Questions and Study Guide

Question: 1 / 400

Solve the exponential equation 2^x = 16.

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4

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 \(

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