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Ch. 4 - Exponential and Logarithmic Functions
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 4 - Exponential and Logarithmic FunctionsProblema 43
Capitolo 5, Problema 43

Use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. ln x + ln 7

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Recall the logarithmic property that states the sum of logarithms with the same base can be written as the logarithm of the product: \(\ln a + \ln b = \ln(ab)\).
Identify the terms in the expression: \(\ln x + \ln 7\); here, \(a = x\) and \(b = 7\).
Apply the property by combining the two logarithms into one: \(\ln(x) + \ln(7) = \ln(x \times 7)\).
Simplify the product inside the logarithm: \(\ln(7x)\).
The expression is now condensed into a single logarithm with coefficient 1: \(\ln(7x)\).

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Properties of Logarithms

Properties of logarithms include rules such as the product, quotient, and power rules. These allow combining or breaking down logarithmic expressions. For example, the product rule states that ln(a) + ln(b) = ln(ab), which helps condense sums of logarithms into a single logarithm.
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Change of Base Property

Natural Logarithm (ln)

The natural logarithm, denoted ln, is the logarithm with base e, where e ≈ 2.718. It is commonly used in calculus and algebra. Understanding ln is essential for manipulating expressions involving exponential growth or decay and applying logarithmic properties correctly.
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The Natural Log

Condensing Logarithmic Expressions

Condensing logarithmic expressions means rewriting multiple logarithms as a single logarithm with a coefficient of 1. This involves applying logarithm properties to combine terms and simplify the expression, making it easier to evaluate or use in further calculations.
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Expand & Condense Log Expressions
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