/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 45 Solve the following equations. ... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 45

Solve the following equations. $$\ln x=-1$$

Short Answer

Expert verified
Answer: The approximate value of x for the equation $$\ln x = -1$$ is 0.368.

Step by step solution

01

Convert the logarithmic equation to exponential form

We start by converting the given equation $$\ln x = -1$$ to exponential form. To do this, we use the fact that if $$\ln x = y$$, then $$x = e^y$$. Therefore, our equation becomes: $$x = e^{-1}$$
02

Simplify the expression #

Now, we'll simplify the expression. Since e is approximately equal to 2.718, $$x = e^{-1}$$ can be simplified by raising e to the power of -1: $$x = \frac{1}{e}$$ Since e is approximately equal to 2.718, we can write the result as: $$x \approx \frac{1}{2.718}$$
03

Find the approximate value of x #

Finally, we'll calculate the approximate value of x by dividing 1 by 2.718: $$x \approx 0.368$$ Thus, the solution to the equation $$\ln x = -1$$ is approximately 0.368.

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