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Chapter 3: Problem 60

Write the exponential equation in logarithmic form. $$e^{2}=7.3890 \ldots$$

Short Answer

Expert verified
\(\ln{7.3890} = 2\)

Step by step solution

01

Identify the variables in the exponential equation

In the given exponential equation \(e^{2}=7.3890\), \(e\) is the base \(b\), \(2\) is the exponential value \(y\), and \(7.3890\) is \(x\).
02

Convert to logarithmic form

Applying the conversion rule from exponential to logarithmic form, \(\log_{b}{x}=y\), we retain \(b\) as the base, \(x\) is the value we take the log of, and \(y\) will be the result. This gives us the equivalent logarithmic form as \(\log_{e}{7.3890} = 2\) or more conventionally \(\ln{7.3890} = 2\)

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Most popular questions from this chapter

Solve the equation algebraically. Round the result to three decimal places. Verify your answer using a graphing utility. $$e^{-2 x}-2 x e^{-2 x}=0$$

The number of bacteria in a culture is increasing according to the law of exponential growth. The initial population is 250 bacteria, and the population after 10 hours is double the population after 1 hour. How many bacteria will there be after 6 hours?

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