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Write each equation in its equivalent exponential form. 5= logb 32
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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 5
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 22x-1=32
Guida verificata passo dopo passo1
Recognize that the equation is \(2^{2x-1} = 32\). The goal is to express both sides as powers of the same base.
Recall that 32 can be written as a power of 2 because \(32 = 2^5\).
Rewrite the equation using this expression: \(2^{2x-1} = 2^5\).
Since the bases are the same and the equation holds true, set the exponents equal to each other: \(2x - 1 = 5\).
Solve the resulting linear equation for \(x\) by isolating \(x\).
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Exponential Equations
An exponential equation is one in which variables appear as exponents. Solving such equations often involves rewriting both sides to have the same base, allowing the exponents to be set equal to each other. This method simplifies the problem to solving a linear equation in the exponent.
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Solving Exponential Equations Using Logs
Expressing Numbers as Powers of the Same Base
To solve exponential equations, it is crucial to rewrite each side as a power of the same base. For example, 32 can be expressed as 2^5 since 2 multiplied by itself 5 times equals 32. This step enables direct comparison of exponents.
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05:10Higher Powers of i
Equating Exponents
Once both sides of an equation have the same base, the exponents can be set equal because if a^m = a^n, then m = n. This principle allows the conversion of an exponential equation into a simpler algebraic equation to solve for the variable.
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04:06Rational Exponents
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