Textbook Question
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
log(1000x)
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Ch. 4 - Exponential and Logarithmic Functions
Chapter 5, Problem 7
In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. e^2.3
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Exponential Functions
Exponential functions are mathematical expressions in the form of f(x) = a * b^x, where 'a' is a constant, 'b' is the base, and 'x' is the exponent. The function e^x, where 'e' is Euler's number (approximately 2.718), is a fundamental exponential function used in various applications, including growth and decay models. Understanding how to evaluate these functions is crucial for solving problems involving exponential growth.
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Exponential Functions
Calculator Usage
Using a calculator effectively is essential for approximating values of complex functions like e^x. Most scientific and graphing calculators have a dedicated 'e' button or function that allows users to compute exponential values directly. Familiarity with the calculator's functions, including how to input exponents and round results, is necessary for accurate calculations.
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Rounding Numbers
Rounding numbers involves adjusting a numerical value to a specified degree of precision, which in this case is three decimal places. This process is important for presenting results in a clear and concise manner, especially in scientific and mathematical contexts. Understanding the rules of rounding, such as when to round up or down, is essential for ensuring that the final answer is both accurate and appropriately formatted.
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Related Practice
Textbook Question
In Exercises 5–9, graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range. f(x) = 3^x and g(x) = -3^x
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Textbook Question
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 4^2x−1=64
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Textbook Question
In Exercises 1–8, write each equation in its equivalent exponential form. log6 216 = y
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Textbook Question
In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
log7 (7/x)
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Textbook Question
In Exercises 5–9, graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function's domain and range. f(x) = e^x and g(x) = 2e^(x/2)
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