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 5 + log 2
1032
views
Ch. 4 - Exponential and Logarithmic Functions
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Not the one you use?Change textbookSelect a different textbook
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 41
Evaluate each expression without using a calculator.
검증된 단계별 안내1
Recognize that the expression is of the form \(a^{\log_a b}\), where the base of the exponent and the base of the logarithm are the same (in this case, 8).
Recall the logarithmic identity: \(a^{\log_a b} = b\). This identity holds because the logarithm \(\log_a b\) is the exponent to which you raise \(a\) to get \(b\).
Apply this identity directly to the expression \(8^{\log_8 19}\), which simplifies to just 19.
Understand that this simplification works without any calculation because the logarithm and the exponent base cancel each other out.
Therefore, the value of the expression \(8^{\log_8 19}\) is simply 19.
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
1m도움이 되었나요?
주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Logarithmic and Exponential Functions
Logarithms and exponents are inverse operations. The logarithm log_b(a) answers the question: to what power must the base b be raised to get a? Understanding this inverse relationship is key to simplifying expressions like b^(log_b(x)).
추천 영상:
5:26
Graphs of Logarithmic Functions
Properties of Logarithms and Exponents
One important property is that b^(log_b(x)) = x, where b is the base of both the exponent and the logarithm. This property allows simplification of expressions where the base of the exponent matches the base of the logarithm.
추천 영상:
5:36Change of Base Property
Evaluating Expressions Without a Calculator
When evaluating expressions like 8^(log_8 19) without a calculator, use algebraic properties to simplify rather than compute directly. Recognizing patterns and applying properties reduces complex expressions to simpler forms.
추천 영상:
가이드 코스
03:11Evaluating Algebraic Expressions
관련 실천
교과서 질문
Graph f(x) = 4x and g(x) = log4 x in the same rectangular coordinate system.
1110
views
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. e2x−3ex+2=0
933
views
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. ln x + ln 7
758
views
교과서 질문
The figure shows the graph of f(x) = ex. In Exercises 35-46, use transformations of this graph to graph each function. Be sure to give equations of the asymptotes. Use the graphs to determine graphs. each function's domain and range. If applicable, use a graphing utility to confirm your hand-drawn h(x) = e-x
1039
views
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. 5(2x+3)=3(x−1)
898
views