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Ch. 4 - Exponential and Logarithmic Functions
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Blitzer 8th EditionCh. 4 - Exponential and Logarithmic Functions문제 45
5장, 문제 45

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. log2 (96) - log2 (3)

검증된 단계별 안내
1
Identify the logarithmic expression given: \(\log_{2}(96) - \log_{2}(3)\).
Recall the logarithmic property for subtraction: \(\log_{a}(x) - \log_{a}(y) = \log_{a}\left(\frac{x}{y}\right)\), where \(a\), \(x\), and \(y\) are positive and \(a \neq 1\).
Apply this property to combine the expression into a single logarithm: \(\log_{2}\left(\frac{96}{3}\right)\).
Simplify the fraction inside the logarithm: calculate \(\frac{96}{3}\) to get a simpler argument for the logarithm.
Rewrite the expression as \(\log_{2}(\text{simplified value})\), which is the condensed form with coefficient 1.

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
2m
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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 or breaking down logarithmic expressions. For example, the quotient rule states that log_b(A) - log_b(B) = log_b(A/B), which is essential for condensing expressions.
추천 영상:
5:36
Change of Base Property

Logarithmic Expression Simplification

Simplifying logarithmic expressions involves rewriting them as a single logarithm with coefficient 1. This often requires applying properties of logarithms and factoring numbers inside the log to simplify or evaluate without a calculator.
추천 영상:
7:30
Logarithms Introduction

Evaluating Logarithms Without a Calculator

Evaluating logarithms without a calculator involves expressing numbers as powers of the base or factoring to simplify. For example, recognizing that 96/3 = 32, and since 32 = 2^5, log_2(32) = 5, allows exact evaluation.
추천 영상:
5:14
Evaluate Logarithms
관련 실천
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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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

Graph f(x) = (1/2)x and g(x) = log1/2 x in the same rectangular coordinate system.

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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. e4x+5e2x−24=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 h(x) = e2x + 1

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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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