교과서 질문
Graph functions f and g in the same rectangular coordinate system. Graph and give equations of all asymptotes. If applicable, use a graphing utility to confirm your hand-drawn graphs. f(x) = 3x and g(x) = 3-x
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Ch. 4 - Exponential and Logarithmic Functions
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- 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
5장, 문제 49
Solve each logarithmic equation in Exercises 49–92. Be sure to reject any value of x that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. log3x=4
검증된 단계별 안내1
Identify the given logarithmic equation: \(\log_{3} x = 4\).
Recall the definition of a logarithm: \(\log_{a} b = c\) means \(a^{c} = b\). Using this, rewrite the equation as \(3^{4} = x\).
Calculate the value of \$3^{4}\( to find \)x$. (You can leave it as an expression for the exact answer.)
Check the domain of the original logarithmic expression. Since \(\log_{3} x\) is defined only for \(x > 0\), ensure your solution satisfies this condition.
If needed, use a calculator to find the decimal approximation of \(x\) to two decimal places.
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
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주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Definition of Logarithms
A logarithm answers the question: to what exponent must the base be raised to produce a given number? For example, log₃(x) = 4 means 3 raised to the power 4 equals x. Understanding this definition allows you to rewrite logarithmic equations in exponential form to solve for the variable.
추천 영상:
7:30
Logarithms Introduction
Domain of Logarithmic Functions
The domain of a logarithmic function log_b(x) includes only positive real numbers (x > 0) because logarithms of zero or negative numbers are undefined. When solving logarithmic equations, it is essential to check that solutions fall within this domain to ensure they are valid.
추천 영상:
5:26Graphs of Logarithmic Functions
Exact and Approximate Solutions
Logarithmic equations often yield exact solutions expressed in exponential form. However, when a decimal approximation is required, a calculator can be used to find a numerical value, typically rounded to a specified number of decimal places, such as two decimals for clarity and precision.
추천 영상:
4:20Graph Hyperbolas at the Origin
관련 실천
교과서 질문
Solve each exponential equation in Exercises 23–48. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 32x+3x−2=0
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교과서 질문
Use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. log x + 3 log y
998
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교과서 질문
Graph functions f and g in the same rectangular coordinate system. Graph and give equations of all asymptotes. If applicable, use a graphing utility to confirm your hand-drawn graphs. f(x) = 3x and g(x) = (1/3). 3x
998
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교과서 질문
In Exercises 50–53, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator.
1099
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교과서 질문
Use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. (1/2)ln x + ln y
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