Domanda del libro di testo
Graph functions f and g in the same rectangular coordinate system. Graph and give equations of all asymptotes. If applicable, use a graphing utility to confirm your hand-drawn graphs. f(x) = 3x and g(x) = 3-x
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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 49
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. log x + 3 log y
Guida verificata passo dopo passo1
Identify the logarithmic expression given: \(\log x + 3 \log y\).
Recall the logarithmic property that allows you to move coefficients as exponents inside the log: \(a \log b = \log b^a\).
Apply this property to the term \(3 \log y\) to rewrite it as \(\log y^3\).
Now the expression becomes \(\log x + \log y^3\).
Use the logarithmic property that the sum of logs is the log of the product: \(\log a + \log b = \log (a \times b)\), so combine to get \(\log (x \times y^3)\).
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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 power rule states that a coefficient in front of a log can be rewritten as an exponent inside the log: a·log b = log(b^a).
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Change of Base Property
Condensing Logarithmic Expressions
Condensing logarithmic expressions means rewriting multiple logs as a single logarithm. This involves applying the product, quotient, and power properties to combine terms into one log with coefficient 1. The goal is to simplify the expression for easier evaluation or further manipulation.
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4:22Expand & Condense Log Expressions
Evaluating Logarithms Without a Calculator
Evaluating logarithms without a calculator often requires recognizing common log values or rewriting expressions using known bases and exponents. Simplifying logs using properties can help express them in terms of simpler or known logarithms, enabling exact evaluation rather than decimal approximation.
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5:14Evaluate Logarithms
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