교과서 질문
Evaluate each expression without using a calculator.
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Ch. 4 - Exponential and Logarithmic Functions
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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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 41
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
검증된 단계별 안내1
Recall the logarithmic property that states the sum of two logarithms with the same base can be written as the logarithm of the product: \(\log a + \log b = \log (a \times b)\).
Identify the terms in the expression: \(\log 5 + \log 2\) both have the same base (common logarithm, base 10).
Apply the property to combine the two logarithms into one: \(\log (5 \times 2)\).
Simplify the product inside the logarithm: \(\log 10\).
Recognize that \(\log 10\) (base 10) equals 1, so the expression simplifies to \(1\).
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Properties of Logarithms
Properties of logarithms include rules such as the product, quotient, and power rules. The product rule states that log(a) + log(b) = log(ab), allowing the combination of sums into a single logarithm. Understanding these properties is essential for condensing expressions into one logarithm.
추천 영상:
5:36
Change of Base Property
Logarithmic Expression Simplification
Simplifying logarithmic expressions involves applying logarithm properties to rewrite sums or differences as a single logarithm. This process often includes removing coefficients by converting them into exponents and combining terms to achieve a single log with coefficient 1.
추천 영상:
7:30Logarithms Introduction
Evaluating Logarithms Without a Calculator
Some logarithmic expressions can be evaluated exactly by recognizing values and their relationships, such as log base 10 of 5 and 2. Multiplying inside the log can yield a number whose log is known or easily simplified, enabling evaluation without a calculator.
추천 영상:
5:14Evaluate Logarithms
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. e2x−3ex+2=0
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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 g(x) = 2ex
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교과서 질문
In Exercises 39–40, 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) = ln x and g(x) = - ln (2x)
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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)
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