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Evaluate or simplify each expression without using a calculator. In e9x
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Ch. 4 - Exponential and Logarithmic Functions
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 5, Problema 95
In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. ln(5x) + ln 1 = ln(5x)
Guida verificata passo dopo passo1
Recall the logarithmic property that states: . This means the sum of two natural logarithms is the natural logarithm of the product of their arguments.
Apply this property to the left side of the equation: .
Recognize that because the natural logarithm of 1 is always zero.
Since the left side simplifies to , and the right side is also , the equation is true as written.
Therefore, no changes are necessary to make the statement true.
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Properties of Logarithms
Logarithms have specific properties that simplify expressions, such as the product rule: ln(a) + ln(b) = ln(ab). Understanding these rules helps in combining or breaking down logarithmic expressions correctly.
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5:36
Change of Base Property
Logarithm of One
The natural logarithm of 1, ln(1), is always 0 because e^0 = 1. Recognizing this fact is essential when simplifying logarithmic expressions involving ln(1).
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7:30Logarithms Introduction
Equation Verification and Simplification
To determine if an equation involving logarithms is true, simplify both sides using logarithmic properties and evaluate constants. This process helps verify the equality or identify necessary corrections.
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06:00Categorizing Linear Equations
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