Domanda del libro di testo
In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 3√5
812
views
Ch. 4 - Exponential and Logarithmic Functions
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
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 3
Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log7 (7x)
Guida verificata passo dopo passo1
Identify the logarithmic expression given: \(\log_{7}(7x)\).
Recall the logarithmic property that states \(\log_b(mn) = \log_b(m) + \log_b(n)\), which allows us to expand the log of a product into a sum of logs.
Apply this property to the expression: \(\log_{7}(7x) = \log_{7}(7) + \log_{7}(x)\).
Evaluate \(\log_{7}(7)\) using the fact that \(\log_b(b) = 1\) for any base \(b\), so \(\log_{7}(7) = 1\).
Write the fully expanded form as \(1 + \log_{7}(x)\), which is the simplified expanded expression.
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
2mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Properties of Logarithms
Properties of logarithms include rules such as the product, quotient, and power rules that allow the expansion or simplification of logarithmic expressions. For example, log_b(MN) = log_b(M) + log_b(N) helps break down complex expressions into simpler parts.
Video consigliato:
5:36
Change of Base Property
Logarithm of a Base Raised to a Power
The logarithm of a base raised to the same base simplifies to the exponent, i.e., log_b(b) = 1. This property is useful for evaluating expressions like log_7(7), which equals 1, simplifying the overall expression.
Video consigliato:
04:10Powers of i
Evaluating Logarithmic Expressions Without a Calculator
Some logarithmic expressions can be evaluated exactly by recognizing patterns or using properties, such as when the argument is a power of the base. This avoids approximation and provides exact values, enhancing understanding of logarithmic behavior.
Video consigliato:
5:14Evaluate Logarithms
Pratica correlata
Domanda del libro di testo
Use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log5 (7 × 3)
928
views
Domanda del libro di testo
The graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 4x, g(x) = 4-x, h(x) = -4-x, r(x) = -4-x+3
1165
views
Domanda del libro di testo
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 5x=125
708
views
Domanda del libro di testo
Write each equation in its equivalent exponential form. 4 = log2 16
1070
views
Domanda del libro di testo
The graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 4x, g(x) = 4-x, h(x) = -4-x, r(x) = -4-x+3
1333
views