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Chapter 3: Problem 64

Evaluate \(g(x)=\ln x\) at the indicated value of \(x\) without using a calculator. $$x=e^{-5 / 2}$$

Short Answer

Expert verified
The output when evaluating \(g(x)=\ln x\) at \(x=e^{-5 / 2}\) is -5/2.

Step by step solution

01

Identifying Elements

Identify the elements in the given exercise. The function is \(g(x) = \ln x\) and the value of \(x\) is indicated as \(e^{-5/2}\). Next, substitute \(x\) with the given value into the function.
02

Substitute the Value of x

Substitute the value of \(x\) in \(g(x) = \ln x\) with the provided \(e^{-5/2}\). The function thus becomes \(g(e^{-5/2}) = \ln (e^{-5/2})\).
03

Simplify the Expression

To simplify the expression, remember the property of logarithms that states \(ln(e^x) = x\). Here, \(x = -5/2\), thus it simplifies to \(g(e^{-5/2}) = -5/2\).

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