SOLVED:Write Each Expression As A Single Logarithm. See Example ...

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Write each expression as a single logarithm. See Example 3. $$\ln (4 h-8)-\ln (4)$$ Write each expression as a single logarithm. See Example 3.$$\ln (4 h-8)-\ln (4)$$ Algebra for College Students Mark Dugopolski 5th Edition Chapter 11, Problem 33 View All Chapters

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Step 1: We start with the given expression $\ln (4 h-8)-\ln (4)$. Show more…

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Key Concepts

Natural Logarithm The natural logarithm is a logarithm with base e, where e is an irrational and transcendental number approximately equal to 2.71828. It serves as a fundamental building block in calculus, differential equations, and many applications in science, providing a natural way of modeling growth and decay processes. Logarithmic Quotient Rule The logarithmic quotient rule is a key property of logarithms which states that the difference between two logarithms can be rewritten as the logarithm of the quotient; that is, ln(a) - ln(b) equals ln(a/b). This property is essential for combining multiple logarithmic expressions into one, as seen in the process of expressing differences of logarithms as a single logarithm. Expression Simplification Expression simplification involves using algebraic techniques such as factoring and reducing terms to rewrite complex expressions in a simpler or more revealing form. In the context of logarithms, it often means recognizing common factors or expressions that allow the application of properties like the quotient rule to combine or condense expressions.

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Transcript

00:02 We want to write this expression as a single logarithm, and we can do that using the quotient rule, which tells us that if we have a log minus a log, it's equivalent to the log of the quotient. 00:13 So here we have a log minus a log. 00:16 We can write it as a natural log of 4h minus 8 over 4... Need help? Use Ace Ace is your personal tutor. It breaks down any question with clear steps so you can learn. Start Using Ace Ace is your personal tutor for learning Step-by-step explanations Instant summaries Summarize YouTube videos Understand textbook images or PDFs Study tools like quizzes and flashcards Listen to your notes as a podcast

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