Domanda del libro di testo
Write each equation in its equivalent logarithmic form. 2-4 = 1/16
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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 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 \(x\).
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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.
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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.
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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.
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04:06Rational Exponents
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