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. 9x=27
666
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 10
Write each equation in its equivalent logarithmic form. 54 = 625
Guida verificata passo dopo passo1
Identify the components of the exponential equation \(5^4 = 625\). Here, the base is 5, the exponent (or power) is 4, and the result is 625.
Recall the definition of logarithms: If \(a^b = c\), then the equivalent logarithmic form is \(\log_a c = b\), where \(a\) is the base, \(b\) is the exponent, and \(c\) is the result.
Apply this definition to the given equation by setting the base of the logarithm to 5, the argument to 625, and the result equal to the exponent 4.
Write the logarithmic form as \(\log_5 625 = 4\).
This expresses the original exponential equation in logarithmic form, showing the relationship between the base, the exponent, and the result.
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:
1mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Exponential and Logarithmic Forms
Exponential and logarithmic forms are two ways to express the same relationship. An equation like a^b = c in exponential form can be rewritten as log_a(c) = b in logarithmic form, where 'a' is the base, 'b' is the exponent, and 'c' is the result.
Video consigliato:
5:02
Solving Logarithmic Equations
Definition of a Logarithm
A logarithm answers the question: to what power must the base be raised to produce a given number? For example, log_5(625) = 4 means 5 raised to the 4th power equals 625. Understanding this definition is key to converting between forms.
Video consigliato:
7:30Logarithms Introduction
Properties of Exponents
Properties of exponents, such as a^m * a^n = a^(m+n), help in manipulating and understanding exponential expressions. Recognizing these properties aids in verifying the correctness of conversions between exponential and logarithmic forms.
Video consigliato:
04:06Rational Exponents
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. log(x/100)
1085
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. 32x=8
697
views
Domanda del libro di testo
In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. f(x) = 4x
1165
views
Domanda del libro di testo
Use the compound interest formulas to solve Exercises 10–11. Suppose that you have \$5000 to invest. Which investment yields the greater return over 5 years: 1.5% compounded semiannually or 1.45% compounded monthly?
1319
views
Domanda del libro di testo
In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. e-0.95
882
views