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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.6: Exponential And Logarithmic Equations
Problem 40E
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![**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**:
\[
\log_2 9 + \frac{1}{2} \log_2 r - \log_2 s
\]
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