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,...
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![### Solving Exponential Equations Using Like Bases
**Problem Statement:**
Use the like bases property to solve the equation:
\[ 6(10)^n = 6000 \]
**Solution:**
To solve this equation, we need to express both sides with like bases, allowing us to equate the exponents effectively.
1. **Equate Bases:**
Break down the equation as follows:
\[ 6 \cdot 10^n = 6000 \]
2. **Simplify:**
Divide both sides of the equation by 6 to isolate the term with the exponent:
\[ 10^n = \frac{6000}{6} \]
\[ 10^n = 1000 \]
3. **Recognize Powers of 10:**
Recognize that \( 1000 = 10^3 \).
4. **Solve for \( n \):**
Since the bases are the same, equate the exponents:
\[ n = 3 \]
Thus, the solution is:
\[ n = 3 \]
---
You can add further explanations and justifications for each step using the "Add Work" feature to deepen understanding.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f6f5faf-b268-40f0-b930-7beeb05513ee%2Fde11a042-04be-45e0-92bf-ea0235c4ec97%2Fus8a2sk_processed.png&w=3840&q=75)
Transcribed Image Text:### Solving Exponential Equations Using Like Bases
**Problem Statement:**
Use the like bases property to solve the equation:
\[ 6(10)^n = 6000 \]
**Solution:**
To solve this equation, we need to express both sides with like bases, allowing us to equate the exponents effectively.
1. **Equate Bases:**
Break down the equation as follows:
\[ 6 \cdot 10^n = 6000 \]
2. **Simplify:**
Divide both sides of the equation by 6 to isolate the term with the exponent:
\[ 10^n = \frac{6000}{6} \]
\[ 10^n = 1000 \]
3. **Recognize Powers of 10:**
Recognize that \( 1000 = 10^3 \).
4. **Solve for \( n \):**
Since the bases are the same, equate the exponents:
\[ n = 3 \]
Thus, the solution is:
\[ n = 3 \]
---
You can add further explanations and justifications for each step using the "Add Work" feature to deepen understanding.
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