Solve 2^x = 16.

Get ready for the Midpoint Summative Exam! Comprehensive flashcards and multiple choice questions await, with hints and detailed explanations. Excel on your test day!

Multiple Choice

Solve 2^x = 16.

Explanation:
When two powers have the same base, equality of the expressions means the exponents must be equal. Here the equation is 2^x = 16. Recognize that 16 is 2^4, since 2^4 = 16. So the equation becomes 2^x = 2^4. With the same base, the only way these are equal is if the exponents match, giving x = 4. You can also see this by taking a log base 2: x = log_2(16) = 4. The other nearby exponents give 2^3 = 8 or 2^5 = 32, which aren’t 16. Therefore, x is 4.

When two powers have the same base, equality of the expressions means the exponents must be equal. Here the equation is 2^x = 16. Recognize that 16 is 2^4, since 2^4 = 16. So the equation becomes 2^x = 2^4. With the same base, the only way these are equal is if the exponents match, giving x = 4. You can also see this by taking a log base 2: x = log_2(16) = 4. The other nearby exponents give 2^3 = 8 or 2^5 = 32, which aren’t 16. Therefore, x is 4.

More Multiple Choice Questions
Subscribe

Get the latest from Passetra

You can unsubscribe at any time. Read our privacy policy