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Ch. 4 - Exponential and Logarithmic Functions
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514당신이 사용하는 게 아니라요?교과서 변경
5장, 문제 35

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. e(5x−3) - 2 =10,476

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Start with the given equation: \(e^{(5x - 3)} - 2 = 10476\).
Isolate the exponential term by adding 2 to both sides: \(e^{(5x - 3)} = 10476 + 2\).
Simplify the right side: \(e^{(5x - 3)} = 10478\).
Take the natural logarithm (ln) of both sides to undo the exponential: \(\ln\left(e^{(5x - 3)}\right) = \ln(10478)\).
Use the logarithm power rule to bring down the exponent: \((5x - 3) = \ln(10478)\), then solve for \(x\) by isolating it: \(5x = \ln(10478) + 3\), and finally \(x = \frac{\ln(10478) + 3}{5}\).

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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.

Exponential Equations

Exponential equations involve variables in the exponent, such as e^(5x−3). Solving these requires isolating the exponential expression and then applying logarithms to both sides to solve for the variable.
추천 영상:
5:47
Solving Exponential Equations Using Logs

Natural and Common Logarithms

Natural logarithms (ln) use base e, while common logarithms (log) use base 10. They are inverse functions of exponential functions and are used to solve equations where the variable is an exponent.
추천 영상:
5:57
Graphs of Common Functions

Using a Calculator for Approximation

After expressing the solution in logarithmic form, calculators help find decimal approximations. This step involves evaluating logarithms and rounding the result to the desired decimal places, such as two decimals.
추천 영상:
5:47
Solving Exponential Equations Using Logs