Question

Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the four answer choices: A symbol that appears more than once in a question has the same meaning throughout the question. \[ 10^x = 10,000,000,000 \]

• A. Quantity A is greater
• B. The relationship cannot be determined from the information given
• C. The two quantities are equal
• D. Quantity B is greater

Hint:

When comparing quantities involving powers of 10, express the numbers in terms of the same base to simplify comparisons.

Answer 1

The Correct Option is D

Step 1: Analyzing the equation.
We are given that \( 10^x = 10,000,000,000 \). First, express \( 10,000,000,000 \) as a power of 10: \[ 10^x = 10^{10}. \]
Step 2: Compare Quantity A and Quantity B.
This implies \( x = 10 \), so \[ \text{Quantity A} = 10, \quad \text{Quantity B} = 12. \]
Step 3: Conclusion.
Clearly, \( 10<12 \), hence Quantity B is greater.