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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 91
5장, 문제 91

Evaluate or simplify each expression without using a calculator. In (1/e6)

검증된 단계별 안내
1
Recognize that the expression is \( \frac{1}{e^{6}} \), which is a fraction with the base \( e \) raised to the power of 6 in the denominator.
Recall the property of exponents that \( \frac{1}{a^{n}} = a^{-n} \), where \( a \) is a nonzero number and \( n \) is an integer.
Apply this property to rewrite \( \frac{1}{e^{6}} \) as \( e^{-6} \).
Understand that \( e^{-6} \) is the simplified form of the original expression, representing the exponential function with a negative exponent.
No further simplification is needed unless the problem asks for a decimal approximation, which is not allowed here.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
1m

주요 개념

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

Properties of Exponents

Understanding how to manipulate expressions with exponents is essential. This includes rules like a^m / a^n = a^(m-n) and (a^m)^n = a^(mn), which help simplify expressions involving powers, especially when dealing with fractions and negative exponents.
추천 영상:
04:06
Rational Exponents

Negative Exponents

A negative exponent indicates the reciprocal of the base raised to the corresponding positive exponent. For example, a^(-n) = 1 / a^n. Recognizing and applying this rule allows simplification of expressions like 1 / e^6 into e^(-6).
추천 영상:
6:37
Zero and Negative Rules

Simplifying Exponential Expressions Without a Calculator

Simplifying expressions without a calculator involves applying exponent rules and algebraic manipulation rather than numerical approximation. This skill is crucial for exact answers and understanding the structure of exponential expressions.
추천 영상:
6:39
Simplifying Exponential Expressions
관련 실천
교과서 질문

Evaluate or simplify each expression without using a calculator. In e6

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교과서 질문

n Exercises 92–93, rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm and then round to three decimal places. y = 73(2.6)^x

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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. ln(x−4)+ln(x+1)=ln(x−8)

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교과서 질문

In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. log4 (2x3) = 3 log4 (2x)

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교과서 질문

Determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement. ln(8x3) = 3 ln (2x)

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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. ln(x−2)−ln(x+3)=ln(x−1)−ln(x+7)

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