Domanda del libro di testo
In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 3√5
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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 3
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
Guida verificata passo dopo passo1
Recognize that the equation is \(5^{x} = 125\). The goal is to express both sides as powers of the same base.
Recall that 125 can be written as a power of 5 because \(125 = 5^{3}\).
Rewrite the equation using this expression: \(5^{x} = 5^{3}\).
Since the bases are the same and the equation holds true, set the exponents equal to each other: \(x = 3\).
This gives the solution for \(x\) without needing to calculate any further.
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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 numbers as powers of a common base. For example, 125 can be expressed as 5³, which allows the equation 5^x = 125 to be rewritten as 5^x = 5^3.
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05:10Higher Powers of i
Equating Exponents
Once both sides of an exponential equation have the same base, the exponents can be set equal to each other because if a^m = a^n, then m = n. This property simplifies solving for the variable in the exponent.
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04:06Rational Exponents
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