Express the given logarithm as a sum and/or difference of logarithms. Simplify, if possible. Assume that all variables represent positive real numbers. log 2 log2s-log29-글 10g2 O log2(9/r) - log2s log29 logzm + log2s log29 + log2r - lo825
Express the given logarithm as a sum and/or difference of logarithms. Simplify, if possible. Assume that all variables represent positive real numbers. log 2 log2s-log29-글 10g2 O log2(9/r) - log2s log29 logzm + log2s log29 + log2r - lo825
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter5: Exponential And Logarithmic Functions
Section5.3: Logarithmic Functions And Their Graphs
Problem 132E
Related questions
Question
100%
![**Objective:** Express the given logarithm as a sum and/or difference of logarithms. Simplify, if possible. Assume that all variables represent positive real numbers.
Given Expression:
\[
\log_2 \left(\frac{9\sqrt{r}}{s}\right)
\]
**Options:**
a) \(\log_2 9 - \frac{1}{2} \log_2 r\)
b) \(\log_2 (9 \sqrt{r}) - \log_2 s\)
c) \(\log_2 9 + \frac{1}{2} \log_2 r - \log_2 s\)
d) \(\log_2 9 + \frac{1}{2} \log_2 r - \log_2 s\)
**Analysis:**
- Use the properties of logarithms to rewrite the expression as a sum and/or difference.
- Properties involved:
1. \(\log_b \left(\frac{m}{n}\right) = \log_b m - \log_b n\)
2. \(\log_b (mn) = \log_b m + \log_b n\)
3. \(\log_b (m^n) = n \log_b m\)
**Correct Simplification:**
The correct formatted expression is option **d**:
\[
\log_2 9 + \frac{1}{2} \log_2 r - \log_2 s
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f1b8d52-12f4-4831-bc71-189b57bb4a76%2Fb9eea463-cceb-49a1-93d9-b316bb4922f8%2Ff7csvz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Objective:** Express the given logarithm as a sum and/or difference of logarithms. Simplify, if possible. Assume that all variables represent positive real numbers.
Given Expression:
\[
\log_2 \left(\frac{9\sqrt{r}}{s}\right)
\]
**Options:**
a) \(\log_2 9 - \frac{1}{2} \log_2 r\)
b) \(\log_2 (9 \sqrt{r}) - \log_2 s\)
c) \(\log_2 9 + \frac{1}{2} \log_2 r - \log_2 s\)
d) \(\log_2 9 + \frac{1}{2} \log_2 r - \log_2 s\)
**Analysis:**
- Use the properties of logarithms to rewrite the expression as a sum and/or difference.
- Properties involved:
1. \(\log_b \left(\frac{m}{n}\right) = \log_b m - \log_b n\)
2. \(\log_b (mn) = \log_b m + \log_b n\)
3. \(\log_b (m^n) = n \log_b m\)
**Correct Simplification:**
The correct formatted expression is option **d**:
\[
\log_2 9 + \frac{1}{2} \log_2 r - \log_2 s
\]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Recommended textbooks for you
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning