교과서 질문
Begin by graphing f(x) = log₂ x. Then use transformations of this graph to graph the given function. What is the vertical asymptote? Use the graphs to determine each function's domain and range. g(x) = log₂ (x + 1)
747
views
Ch. 4 - Exponential and Logarithmic Functions
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
당신이 사용하는 게 아니라요?교과서 변경다른 교과서를 선택하세요
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
5장, 문제 53
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. 2 logb x + 3 logb y
검증된 단계별 안내1
Identify the given expression: \(2 \log_{b} x + 3 \log_{b} y\).
Recall the logarithmic property that allows you to move coefficients as exponents inside the logarithm: \(a \log_{b} M = \log_{b} (M^{a})\).
Apply this property to each term: \(2 \log_{b} x = \log_{b} (x^{2})\) and \(3 \log_{b} y = \log_{b} (y^{3})\).
Use the logarithmic property for addition: \(\log_{b} A + \log_{b} B = \log_{b} (A \times B)\) to combine the two terms into a single logarithm.
Write the final condensed expression as \(\log_{b} (x^{2} y^{3})\), which is a single logarithm with coefficient 1.
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
2m도움이 되었나요?
주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Properties of Logarithms
Properties of logarithms include rules such as the product, quotient, and power rules. These allow combining multiple logarithmic terms into a single logarithm by converting coefficients into exponents and combining sums or differences into products or quotients.
추천 영상:
5:36
Change of Base Property
Power Rule of Logarithms
The power rule states that a coefficient in front of a logarithm can be rewritten as an exponent inside the logarithm, i.e., a·log_b(x) = log_b(x^a). This is essential for condensing expressions with coefficients into a single logarithm.
추천 영상:
가이드 코스
5:50Power Rules
Condensing Logarithmic Expressions
Condensing logarithmic expressions means rewriting a sum or difference of logarithms as a single logarithm. This involves applying the product or quotient rules after using the power rule to handle coefficients, simplifying the expression into one logarithm with coefficient 1.
추천 영상:
4:22Expand & Condense Log Expressions
관련 실천
교과서 질문
Use the compound interest formulas A = P (1+ r/n)nt and A =Pert to solve exercises 53-56. Round answers to the nearest cent. Find the accumulated value of an investment of \$10,000 for 5 years at an interest rate of 1.32% if the money is b. compounded quarterly
1648
views
교과서 질문
Use the compound interest formulas A = P (1+ r/n)nt and A =Pert to solve exercises 53-56. Round answers to the nearest cent. Find the accumulated value of an investment of \$10,000 for 5 years at an interest rate of 1.32% if the money is a. compounded semiannually
1106
views
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. log4(x+5)=3
952
views
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. ln x=2
850
views
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.
1064
views