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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 59
5장, 문제 59

In Exercises 58–59, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. log4 0.863

검증된 단계별 안내
1
Recognize that the problem asks for the logarithm of 0.863 with base 4, written as \(\log_{4} 0.863\).
Recall the change of base formula for logarithms: \(\log_{a} b = \frac{\log_{c} b}{\log_{c} a}\), where \(c\) can be any positive number (commonly 10 or \(e\)).
Apply the change of base formula using common logarithms (base 10): \(\log_{4} 0.863 = \frac{\log_{10} 0.863}{\log_{10} 4}\).
Use a calculator to find the values of \(\log_{10} 0.863\) and \(\log_{10} 4\) separately, making sure to keep the values to at least four decimal places.
Divide the two logarithm values obtained in the previous step to get the value of \(\log_{4} 0.863\), rounded to four decimal places.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Logarithms and Their Bases

A logarithm answers the question: to what power must the base be raised to produce a given number? In this problem, log base 4 of 0.863 means finding the exponent x such that 4^x = 0.863. Understanding the relationship between exponents and logarithms is fundamental.
추천 영상:
7:30
Logarithms Introduction

Change of Base Formula

Since calculators typically only compute logarithms with base 10 (common logs) or base e (natural logs), the change of base formula allows conversion: log_b(a) = log_c(a) / log_c(b), where c is 10 or e. This formula enables evaluating log base 4 of 0.863 using a calculator.
추천 영상:
5:36
Change of Base Property

Using a Calculator for Logarithms

Calculators can compute common logarithms (log base 10) and natural logarithms (log base e). By applying the change of base formula, you input log(0.863) divided by log(4) or ln(0.863) divided by ln(4) to find the value. Rounding the result to four decimal places completes the evaluation.
추천 영상:
7:30
Logarithms Introduction
관련 실천
교과서 질문

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교과서 질문

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교과서 질문

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교과서 질문

Graph y= 2x and x = 2y in the same rectangular coordinate system.

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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. log4(3x+2)=3

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교과서 질문

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