교과서 질문
Give the equation of each exponential function whose graph is shown.
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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 63
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. 6+2 ln x=5
검증된 단계별 안내1
Start with the given equation: \(6 + 2 \ln x = 5\).
Isolate the logarithmic term by subtracting 6 from both sides: \(2 \ln x = 5 - 6\).
Simplify the right side: \(2 \ln x = -1\).
Divide both sides by 2 to solve for \(\ln x\): \(\ln x = \frac{-1}{2}\).
Rewrite the equation in exponential form to solve for \(x\): \(x = e^{\frac{-1}{2}}\).
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.
Properties of Logarithms
Understanding the properties of logarithms, such as the natural logarithm (ln) and its relationship to exponents, is essential. For example, ln(x) is the power to which e must be raised to get x. These properties help in isolating the logarithmic term and simplifying the equation.
추천 영상:
5:36
Change of Base Property
Domain of Logarithmic Functions
The domain of a logarithmic function ln(x) is x > 0 because the logarithm of zero or a negative number is undefined. When solving logarithmic equations, it is crucial to check that the solutions fall within this domain to reject extraneous or invalid answers.
추천 영상:
5:26Graphs of Logarithmic Functions
Solving Logarithmic Equations
Solving logarithmic equations often involves isolating the logarithm, rewriting the equation in exponential form, and then solving for the variable. After finding potential solutions, verify them against the domain restrictions to ensure they are valid.
추천 영상:
5:02Solving Logarithmic Equations
관련 실천
교과서 질문
In Exercises 60–63, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. (log2 x)^4 = 4 log2 x
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교과서 질문
The figure shows the graph of f(x) = log x. In Exercises 59–64, use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range.
g(x) = 1-log x
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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)(log x + log y)
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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. 3 ln x + 5 ln y - 6 ln z
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교과서 질문
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. 5 ln(2x)=20
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