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)
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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 1
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 2x=64
Guida verificata passo dopo passo1
Identify the bases on both sides of the equation: the left side is already base 2, and the right side is 64.
Express 64 as a power of 2. Since 64 is a power of 2, write 64 as \$2^{n}$ where $n$ is an integer.
Rewrite the equation using the same base: \(2^{x} = 2^{n}\).
Since the bases are the same and the equation holds true, set the exponents equal to each other: \(x = n\).
Solve for \(x\) by determining the value of \(n\) from the expression of 64 as a power of 2.
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Exponential Equations
An exponential equation is one in which variables appear as exponents. Solving these equations often involves rewriting both sides with the same base to compare the exponents directly.
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Solving Exponential Equations Using Logs
Expressing Numbers as Powers of the Same Base
To solve exponential equations, rewrite each number as a power of a common base. For example, 64 can be expressed as 2^6, allowing the equation 2^x = 2^6 to be solved by equating exponents.
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Equating Exponents
Once both sides of an exponential equation have the same base, the exponents can be set equal to each other. This reduces the problem to solving a simpler algebraic equation involving the exponents.
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04:06Rational Exponents
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