Algebra and Trigonometry (6th Edition)
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 \( x \).
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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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