Write the following expression as a sum and/or difference of logarithms. Express powers as factors. x+3 In 4x e X+3 In = In x+3-4x (Simplify your answer.) e 4x
Write the following expression as a sum and/or difference of logarithms. Express powers as factors. x+3 In 4x e X+3 In = In x+3-4x (Simplify your answer.) e 4x
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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![**Problem: Simplifying Logarithmic Expressions**
Write the following expression as a sum and/or difference of logarithms. Express powers as factors.
\[
\ln\left(\frac{x+3}{e^{4x}}\right)
\]
**Solution:**
Using the properties of logarithms, we can express the given expression as:
\[
\ln(x+3) - \ln(e^{4x})
\]
Since \(\ln(e^{4x}) = 4x\), we further simplify:
\[
\ln(x+3) - 4x
\]
Thus, the simplified expression is: \(\ln(x+3) - 4x\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F220fbd20-0469-420e-b941-1fe3bddd2a34%2F3100f8ac-f16b-4278-bfc5-ed3efc63abe1%2F8oigb88_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem: Simplifying Logarithmic Expressions**
Write the following expression as a sum and/or difference of logarithms. Express powers as factors.
\[
\ln\left(\frac{x+3}{e^{4x}}\right)
\]
**Solution:**
Using the properties of logarithms, we can express the given expression as:
\[
\ln(x+3) - \ln(e^{4x})
\]
Since \(\ln(e^{4x}) = 4x\), we further simplify:
\[
\ln(x+3) - 4x
\]
Thus, the simplified expression is: \(\ln(x+3) - 4x\).
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