Domanda del libro di testo
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
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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
In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 23.4
Guida verificata passo dopo passo1
Identify the expression to evaluate: \$2^{3.4}$.
Recall that \(a^b\) means \(a\) raised to the power of \(b\), where \(a=2\) and \(b=3.4\) in this case.
Use a calculator to compute \$2^{3.4}$. Most calculators have a power function, often labeled as $x^y$ or \(\hat{}\).
Enter 2, then use the power function, and then enter 3.4 to get the approximate value.
Round the result to three decimal places as instructed.
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Exponents and Powers
Exponents indicate how many times a base number is multiplied by itself. For example, 2^3 means 2 multiplied by itself 3 times (2 × 2 × 2). Understanding how to interpret and work with exponents is essential for evaluating expressions like 2^3.4.
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Percorso guidato
04:10
Powers of i
Decimal Exponents
Decimal exponents represent roots and fractional powers, extending the idea of integer exponents. For instance, 2^3.4 means 2 raised to a power between 3 and 4, which can be calculated using logarithms or a calculator. This concept helps in approximating values that are not whole-number powers.
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Percorso guidato
04:06Rational Exponents
Rounding to a Specified Decimal Place
Rounding is the process of limiting a number to a certain number of decimal places for simplicity and clarity. Rounding to three decimal places means keeping three digits after the decimal point and adjusting the last digit based on the next digit. This ensures the answer is precise yet manageable.
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4:47The Number e
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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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The graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 4x, g(x) = 4-x, h(x) = -4-x, r(x) = -4-x+3
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Domanda del libro di testo
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
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Domanda del libro di testo
Write each equation in its equivalent exponential form. 4 = log2 16
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The graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 4x, g(x) = 4-x, h(x) = -4-x, r(x) = -4-x+3
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