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Chapter 3: Problem 51

Write the logarithmic equation in exponential form. $$\ln \frac{1}{2}=-0.693 \ldots$$

Short Answer

Expert verified
The given logarithmic equation in exponential form is \( e^{-0.693} = \frac{1}{2} \).

Step by step solution

01

Understand the Logarithm

The base of a logarithm in the form of \( \ln \) is \( e \). Logarithm is another way to express exponent numbers. So this says: \( e \) raised to the power of, the answer we get is equal to the argument of the logarithm. In this case the argument is \( \frac{1}{2} \).
02

Convert the logarithmic form to exponential form

According to the property of logarithms, we can rewrite the equation \( \ln \frac{1}{2}=-0.693 \) as \( e^{-0.693} = \frac{1}{2} \). This is an exponential form of the given logarithmic equation.

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Most popular questions from this chapter

The amount of time (in hours per week) a student utilizes a math-tutoring center roughly follows the normal distribution \(y=0.7979 e^{-(x-5.4)^{2} / 0.5},\) \(4 \leq x \leq 7,\) where \(x\) is the number of hours. (a) Use a graphing utility to graph the function. (b) From the graph in part (a), estimate the average number of hours per week a student uses the tutoring center.

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Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$4 \log (x-6)=11$$
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