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Ch. 4 - Exponential and Logarithmic Functions
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 4 - Exponential and Logarithmic FunctionsProblema 21
Capitolo 5, Problema 21

Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. e(x+1)=1/e

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Rewrite the right side of the equation \(e^{(x+1)} = \frac{1}{e}\) as a power of \(e\). Since \(\frac{1}{e} = e^{-1}\), the equation becomes \(e^{(x+1)} = e^{-1}\).
Now that both sides have the same base \(e\), set the exponents equal to each other: \(x + 1 = -1\).
Solve the resulting linear equation for \(x\) by isolating \(x\): subtract 1 from both sides to get \(x = -1 - 1\).
Simplify the right side to find the value of \(x\).
Verify your solution by substituting \(x\) back into the original equation to ensure both sides are equal.

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An exponential function has the form a^x, where the base a is a positive constant. Understanding how to manipulate and interpret these functions is essential for solving equations involving exponents, especially when the variable is in the exponent.
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The number e is a special irrational constant approximately equal to 2.718. Understanding that 1/e can be written as e^(-1) helps rewrite the equation with the same base, enabling the use of exponent rules to solve for the variable.
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