Domanda del libro di testo
Write each equation in its equivalent logarithmic form. 2-4 = 1/16
858
views
1
rank
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 11
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
Guida verificata passo dopo passo1
Identify the bases of the exponential expressions on both sides of the equation: \(9^x = 27\).
Express both 9 and 27 as powers of the same base. Since both are powers of 3, write \(9 = 3^2\) and \(27 = 3^3\).
Rewrite the equation using these expressions: \((3^2)^x = 3^3\).
Apply the power of a power property by multiplying the exponents: \(3^{2x} = 3^3\).
Since the bases are the same and the expressions are equal, set the exponents equal to each other: \(2x = 3\), then solve for \(x\).
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 Equations
An exponential equation is one in which variables appear as exponents. Solving these equations often involves rewriting expressions so that both sides have the same base, allowing the exponents to be set equal to each other.
Video consigliato:
Percorso guidato
5:47
Solving Exponential Equations Using Logs
Expressing Numbers as Powers of the Same Base
To solve exponential equations, it is helpful to rewrite each number as a power of a common base. For example, 9 can be written as 3² and 27 as 3³, enabling comparison of exponents when bases match.
Video consigliato:
Percorso guidato
05:10Higher Powers of i
Equating Exponents
Once both sides of an equation have the same base, the exponents can be set equal to each other because if a^m = a^n, then m = n. This principle simplifies solving for the variable in the exponent.
Video consigliato:
Percorso guidato
04:06Rational Exponents
Pratica correlata
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
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. log4 (64/y)
904
views
Domanda del libro di testo
Write each equation in its equivalent logarithmic form. 54 = 625
801
views