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Chapter 4: Problem 26

Solve each exponential equation. 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. $$e^{x}=0.83$$

Short Answer

Expert verified
The solution to the equation \(e^{x} = 0.83\) is \(x = \ln(0.83)\), which is approximately -0.19 after rounding to two decimal places.

Step by step solution

01

Rewrite in logarithmic form

To start solving the problem, we first change the equation from exponential form to logarithmic form. Using the definition of a logarithm, we can write this as \(x = \ln(0.83)\).
02

Use a calculator to find decimal solution

In the second step, use a calculator to find the decimal equivalent of \(x\), rounded to two decimal places.

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Most popular questions from this chapter

The percentage of adult height attained by a girl who is \(x\) years old can be modeled by $$f(x)=62+35 \log (x-4)$$ where \(x\) represents the girl's age (from 5 to 15 ) and \(f(x)\) represents the percentage of her adult height. Round answers to the nearest tenth of a percent. Approximately what percentage of her adult height has a girl attained at age \(13 ?\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. \(\log _{b} x\) is the exponent to which \(b\) must be raised to obtain \(x\).

he formula \(A=10 e^{-0.003 t}\) models the population of Hungary, \(A\), in millions, \(t\) years after 2006 . a. Find Hungary's population, in millions, for \(2006,2007\), \(2008,\) and \(2009 .\) Round to two decimal places. b. Is Hungary's population increasing or decreasing?

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