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Ch. 1 - Functions
Briggs - Calculus: Early Transcendentals 3rd Edition
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Briggs 3rd EditionCh. 1 - Functions문제 1.42
1장, 문제 1.42

Solve each equation.
48=6e4k48=6e^{4k}

검증된 단계별 안내
1
Start by isolating the exponential term. Divide both sides of the equation by 6 to get: \( e^{4k} = \frac{48}{6} \).
Simplify the right side of the equation: \( e^{4k} = 8 \).
To solve for \( k \), take the natural logarithm of both sides: \( \ln(e^{4k}) = \ln(8) \).
Use the property of logarithms that \( \ln(e^x) = x \) to simplify the left side: \( 4k = \ln(8) \).
Finally, solve for \( k \) by dividing both sides by 4: \( k = \frac{\ln(8)}{4} \).

비슷한 문제에 대한 검증된 영상 답변:

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.

Exponential Functions

Exponential functions are mathematical expressions in the form of f(x) = a * e^(bx), where 'e' is the base of natural logarithms, approximately equal to 2.71828. These functions model growth or decay processes and are characterized by their rapid increase or decrease. Understanding how to manipulate and solve equations involving exponential functions is crucial for solving problems like the one presented.
추천 영상:
6:13
Exponential Functions

Logarithms

Logarithms are the inverse operations of exponentiation, allowing us to solve for the exponent in equations of the form a^x = b. The natural logarithm, denoted as ln, specifically deals with the base 'e'. In the context of the given equation, applying logarithms helps isolate the variable 'k' by transforming the exponential equation into a linear form, making it easier to solve.
추천 영상:
7:30
Logarithms Introduction

Algebraic Manipulation

Algebraic manipulation involves rearranging and simplifying equations to isolate variables or solve for unknowns. This includes operations such as addition, subtraction, multiplication, division, and applying properties of equality. In the context of the given equation, effective algebraic manipulation is necessary to isolate 'e^(4k)' and subsequently apply logarithmic properties to find the value of 'k'.
추천 영상:
05:25
Determine Continuity Algebraically
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