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Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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![### Solving Exponential Equations for Educational Purposes
#### Problem Statement:
Solve for \( x \):
\[ (x - 2)^{7/3} = 128 \]
\[ x = \]
#### Explanation:
To solve this equation, we need to isolate \( x \). Follow these steps:
1. **Identify the exponential part**: We see the term \((x - 2)^{7/3}\).
2. **Isolate the base term**: Remove the exponent by raising both sides of the equation to the reciprocal of \(\frac{7}{3}\).
3. **Calculate**: Proceed with finding the numerical value through algebraic manipulation.
This involves recognizing the relationship between exponents and roots, and using algebraic properties to isolate \( x \).
Solving such problems helps students understand the manipulation of exponents and roots, which are critical in algebra and higher-level mathematics. Complete the solution to find the value of \( x \).](https://content.bartleby.com/qna-images/question/4ed3be98-469b-4630-9026-6d8c89f34a56/6afb144d-1a96-46ad-997e-5ed6f64083d2/ji09y8_thumbnail.png)
Transcribed Image Text:### Solving Exponential Equations for Educational Purposes
#### Problem Statement:
Solve for \( x \):
\[ (x - 2)^{7/3} = 128 \]
\[ x = \]
#### Explanation:
To solve this equation, we need to isolate \( x \). Follow these steps:
1. **Identify the exponential part**: We see the term \((x - 2)^{7/3}\).
2. **Isolate the base term**: Remove the exponent by raising both sides of the equation to the reciprocal of \(\frac{7}{3}\).
3. **Calculate**: Proceed with finding the numerical value through algebraic manipulation.
This involves recognizing the relationship between exponents and roots, and using algebraic properties to isolate \( x \).
Solving such problems helps students understand the manipulation of exponents and roots, which are critical in algebra and higher-level mathematics. Complete the solution to find the value of \( x \).
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