Solve: 1. log, (x-2) = 1

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Logarithmic Equations Practice**

Solve the following logarithmic equations:

1. \( \log_4 (x - 2) = 1 \)

2. \( \log_5 (x - 3) = 1 \)

3. \( \log_6 (x + 3) = 1 \)

4. \( \log_3 (x - 8) = 3 \)

5. \( \log_7 (x + 6) = 2 \)

6. \( \log_2 (x - 4) = -3 \)

   Options:
   - [A] \( \frac{33}{8} \)
   - [B] 2
   - [C] 13
   - [D] \( \frac{31}{8} \)

7. \( \log_3 (x - 2) = -1 \)

   Options:
   - [A] \( \frac{11}{5} \)
   - [B] 1
   - [C] \( -\frac{9}{5} \)
   - [D] 5

8. \( \log_5 (x - 3) = -1 \)

   Options:
   - [A] 2
   - [B] \( \frac{10}{3} \)
   - [C] \( \frac{8}{3} \)
   - [D] 9

9. \( \log_2 (x + 8) = -3 \)

   Options:
   - [A] 1
   - [B] \( \frac{65}{8} \)
   - [C] \( \frac{1}{2048} \)
   - [D] \( -\frac{63}{8} \)

10. \( \log_4 (x + 1) = -2 \)

    Options:
    - [A] \( -\frac{15}{16} \)
    - [B] 15
    - [C] \( \frac{17}{16} \)
    - [D] \( \frac{1}{64} \)

**Note**: The problems above involve solving logarithmic equations for the variable \( x \). Each equation is set equal to a constant, requiring the use of properties of logarithms to find the solution. The
Transcribed Image Text:**Logarithmic Equations Practice** Solve the following logarithmic equations: 1. \( \log_4 (x - 2) = 1 \) 2. \( \log_5 (x - 3) = 1 \) 3. \( \log_6 (x + 3) = 1 \) 4. \( \log_3 (x - 8) = 3 \) 5. \( \log_7 (x + 6) = 2 \) 6. \( \log_2 (x - 4) = -3 \) Options: - [A] \( \frac{33}{8} \) - [B] 2 - [C] 13 - [D] \( \frac{31}{8} \) 7. \( \log_3 (x - 2) = -1 \) Options: - [A] \( \frac{11}{5} \) - [B] 1 - [C] \( -\frac{9}{5} \) - [D] 5 8. \( \log_5 (x - 3) = -1 \) Options: - [A] 2 - [B] \( \frac{10}{3} \) - [C] \( \frac{8}{3} \) - [D] 9 9. \( \log_2 (x + 8) = -3 \) Options: - [A] 1 - [B] \( \frac{65}{8} \) - [C] \( \frac{1}{2048} \) - [D] \( -\frac{63}{8} \) 10. \( \log_4 (x + 1) = -2 \) Options: - [A] \( -\frac{15}{16} \) - [B] 15 - [C] \( \frac{17}{16} \) - [D] \( \frac{1}{64} \) **Note**: The problems above involve solving logarithmic equations for the variable \( x \). Each equation is set equal to a constant, requiring the use of properties of logarithms to find the solution. The
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