Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
Bartleby Related Questions Icon

Related questions

Q: logn=log,81 +log,25
A:
Q: Write the equation in logarithmic form. 10³ = 1000 Ⓒlog 1000 = 3 Ⓒlog 3 = 10 1000 = log 3
A:
Q: [(a) √5 3 C A correct expansion of the expression log, is
A:
Q: I. LOGARITHMIC FUNCTIONS. Find the EXPANDED FORM of the following Logarithmic Functions. 1. In 3x 2.…
A:
Q: Expand the logarithimic expression.
A: To expand the logarithmic expression: log5x21-5x32x3-x Solution: Properties of logarithmic…
Q: The expression log a³ + 3 loge(cb4) -7, where c, a, b > 1, written as a single logarithm, is…
A:
Q: Write as the sum and/or difference of logarithms. Express powers as factors. Find logs if logs11 = a…
A: logcab=logca-logcb
Question
**Expand the Logarithmic Expression Fully** Write the given logarithmic expression as a sum or difference of logarithms. **Expression:** \[ \log_2 \left( \frac{y^5 \sqrt{x}}{z^9} \right) \] --- **Explanation:** The expression involves a logarithm with a quotient, power, and root. We'll use the properties of logarithms to expand it: - **Quotient Rule:** \(\log_b \left(\frac{M}{N}\right) = \log_b M - \log_b N\) - **Power Rule:** \(\log_b (M^p) = p \cdot \log_b M\) - **Root as a Power:** \(\sqrt[n]{M} = M^{1/n}\) Using these rules, we can expand the expression as follows: 1. Apply the quotient rule: \[ \log_2 \left( \frac{y^5 \sqrt{x}}{z^9} \right) = \log_2 (y^5 \sqrt{x}) - \log_2 (z^9) \] 2. Apply the power rule separately to \(y^5\) and \(z^9\): \[ \log_2 (y^5 \sqrt{x}) = \log_2 (y^5) + \log_2 (\sqrt{x}) \] \[ \log_2 (y^5) = 5 \cdot \log_2 y \] \[ \log_2 (z^9) = 9 \cdot \log_2 z \] 3. Express \(\sqrt{x}\) as \(x^{1/2}\) and apply the power rule: \[ \log_2 (\sqrt{x}) = \log_2 (x^{1/2}) = \frac{1}{2} \cdot \log_2 x \] 4. Substitute back to get the fully expanded expression: \[ 5 \cdot \log_2 y + \frac{1}{2} \cdot \log_2 x - 9 \cdot \log_2 z \] Thus, the expanded form of the logarithmic expression is: \[ 5 \cdot \log
expand button
Transcribed Image Text:**Expand the Logarithmic Expression Fully** Write the given logarithmic expression as a sum or difference of logarithms. **Expression:** \[ \log_2 \left( \frac{y^5 \sqrt{x}}{z^9} \right) \] --- **Explanation:** The expression involves a logarithm with a quotient, power, and root. We'll use the properties of logarithms to expand it: - **Quotient Rule:** \(\log_b \left(\frac{M}{N}\right) = \log_b M - \log_b N\) - **Power Rule:** \(\log_b (M^p) = p \cdot \log_b M\) - **Root as a Power:** \(\sqrt[n]{M} = M^{1/n}\) Using these rules, we can expand the expression as follows: 1. Apply the quotient rule: \[ \log_2 \left( \frac{y^5 \sqrt{x}}{z^9} \right) = \log_2 (y^5 \sqrt{x}) - \log_2 (z^9) \] 2. Apply the power rule separately to \(y^5\) and \(z^9\): \[ \log_2 (y^5 \sqrt{x}) = \log_2 (y^5) + \log_2 (\sqrt{x}) \] \[ \log_2 (y^5) = 5 \cdot \log_2 y \] \[ \log_2 (z^9) = 9 \cdot \log_2 z \] 3. Express \(\sqrt{x}\) as \(x^{1/2}\) and apply the power rule: \[ \log_2 (\sqrt{x}) = \log_2 (x^{1/2}) = \frac{1}{2} \cdot \log_2 x \] 4. Substitute back to get the fully expanded expression: \[ 5 \cdot \log_2 y + \frac{1}{2} \cdot \log_2 x - 9 \cdot \log_2 z \] Thus, the expanded form of the logarithmic expression is: \[ 5 \cdot \log
Expert Solution
Check Mark
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
See solutionCheck out a sample Q&A here
Step 1: Given expression:
VIEW
Step 2: Find values:
VIEW
Solution
VIEW
bartleby

Step by stepSolved in 3 steps with 3 images

See solution
Check out a sample Q&A here
Blurred answer
Knowledge Booster
Background pattern image
Recommended textbooks for you
Text book image
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:PEARSON
Text book image
Contemporary Abstract Algebra
Algebra
ISBN:9781305657960
Author:Joseph Gallian
Publisher:Cengage Learning
Text book image
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Text book image
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:9780135163078
Author:Michael Sullivan
Publisher:PEARSON
Text book image
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:9780980232776
Author:Gilbert Strang
Publisher:Wellesley-Cambridge Press
Text book image
College Algebra (Collegiate Math)
Algebra
ISBN:9780077836344
Author:Julie Miller, Donna Gerken
Publisher:McGraw-Hill Education
SEE MORE TEXTBOOKS