Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
Need to know if it’s A B C OR D
![**Solve for x**
\[ 10^{x-7} = 1000 \]
**Options:**
- \( \text{A) } x = -4 \)
- \( \text{B) } x = 3 \)
- \( \text{C) } x = 6 \)
- \( \text{D) } x = 10 \)
**Explanation:**
To solve for \( x \) in this equation, follow these steps:
1. Recognize that \( 1000 \) can be expressed as a power of 10:
\[ 1000 = 10^3 \]
2. Therefore, rewrite the equation as:
\[ 10^{x-7} = 10^3 \]
3. Since the bases are the same, set the exponents equal to each other:
\[ x - 7 = 3 \]
4. Solve for \( x \):
\[ x = 3 + 7 \]
\[ x = 10 \]
Thus, the correct answer is:
- \( \text{D) } x = 10 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F45e4ee6c-a715-4803-9fbe-92a41a442b45%2F25b7aabf-8af1-4ad3-910d-03a6127a4789%2F9vbmcjo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Solve for x**
\[ 10^{x-7} = 1000 \]
**Options:**
- \( \text{A) } x = -4 \)
- \( \text{B) } x = 3 \)
- \( \text{C) } x = 6 \)
- \( \text{D) } x = 10 \)
**Explanation:**
To solve for \( x \) in this equation, follow these steps:
1. Recognize that \( 1000 \) can be expressed as a power of 10:
\[ 1000 = 10^3 \]
2. Therefore, rewrite the equation as:
\[ 10^{x-7} = 10^3 \]
3. Since the bases are the same, set the exponents equal to each other:
\[ x - 7 = 3 \]
4. Solve for \( x \):
\[ x = 3 + 7 \]
\[ x = 10 \]
Thus, the correct answer is:
- \( \text{D) } x = 10 \)
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