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. log7 (7x)
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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
In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 3√5
Guida verificata passo dopo passo1
Identify the expression to approximate: \(3^{\sqrt{5}}\) means 3 raised to the power of the square root of 5.
Calculate the square root of 5 using a calculator: find \(\sqrt{5}\).
Use the value of \(\sqrt{5}\) as the exponent and calculate \(3^{\text{(value of } \sqrt{5} \text{)}}\) using the calculator's exponentiation function.
Round the result to three decimal places as requested.
Write the final rounded value as the approximate answer.
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Exponents and Radicals
Exponents represent repeated multiplication, while radicals are the inverse operation, indicating roots. Understanding how to interpret expressions like 3 raised to the root of 5 is essential for evaluating such expressions accurately.
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04:06
Rational Exponents
Using a Calculator for Approximation
Calculators can approximate values of expressions involving irrational numbers or roots. Knowing how to input roots and exponents correctly ensures accurate results, especially when exact values are not easily simplified.
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5:47Solving Exponential Equations Using Logs
Rounding to a Specified Decimal Place
Rounding involves adjusting 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's value.
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4:47The Number e
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