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Chapter 3: Problem 73

Evaluate \(g(x)=\ln x\) at the indicated value of \(x\) without using a calculator. $$x=e^{-5 / 6}$$

Short Answer

Expert verified
The evaluated value of the function \(g(x)=\ln x\) at \(x=e^{-5 / 6}\) is \(-5/6\).

Step by step solution

01

Write down the given value

We have \(x = e^{-5/6}\) and we need to evaluate \(g(x)\) at this point.
02

Evaluate the function

We need to plug in the given value in the logarithmic function. So the function at the given value of \(x\) will be \(g(e^{-5/6}) = \ln(e^{-5/6})\).
03

Use properties of logarithm

Using the property of logarithm \(\ln e^n = n\), we can simplify \(\ln(e^{-5/6})\) as \(-5/6\). Thus, \(g(e^{-5/6}) = -5/6\).

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