Solve for x: 2^x = 16.

Solve for x: 2^x = 16.

• A. 2
• B. 4
• C. 8
• D. 16

Answer: (B)

When two expressions have the same base, their exponents must match if the expressions are equal. Here, 16 can be written as 2^4, so the equation becomes 2^x = 2^4. With the same base, the exponents are equal, so x = 4. Checking: 2^4 indeed equals 16, so this works. The other possibilities don’t work because they yield 4, 256, or 65,536 when plugged into 2^x, not 16.

When two expressions have the same base, their exponents must match if the expressions are equal. Here, 16 can be written as 2^4, so the equation becomes 2^x = 2^4. With the same base, the exponents are equal, so x = 4. Checking: 2^4 indeed equals 16, so this works. The other possibilities don’t work because they yield 4, 256, or 65,536 when plugged into 2^x, not 16.