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Chapter 3: Problem 45

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\ln x=-3$$

Short Answer

Expert verified
The exact value of x is \(e^{-3}\). This can be approximated as 0.050 using a calculator with three decimal places.

Step by step solution

01

Understand the Problem

We have a logarithmic equation, \(ln(x) = -3\). We need to find the value of x for which this equation holds true. The base of the natural logarithm is e (Euler's number, approximately equal to 2.71828).
02

Convert the logarithm to an exponential form

The logarithmic equation \(ln(x) = -3\) translates to \(x = e^{-3}\), when converted to the exponential form.
03

Calculate the value of x

To calculate x, we need to calculate the value of \(e^{-3}\).

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