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Chapter 3: Problem 63

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

Short Answer

Expert verified
The value of \(g(e^{-5/6})\) is \(-5/6\).

Step by step solution

01

Recognize the Inverse Property

Start by recognizing the inverse property between the exponential function and the natural logarithm function. This property means that the natural logarithm of \(e^y\) is just \(y\). In simpler terms, \(\ln(e^y) = y\).
02

Substitute the Value of x

Next, substitute the given value of \(x=e^{-5/6}\) into the function \(g(x) = \ln x\). This gives you \(g(e^{-5/6})\).
03

Apply the Inverse Property

Now, apply the inverse property. You substitute \(y=-5/6\) into \(\ln(e^y) = y\). That will give you \(\ln(e^{-5/6}) = -5/6\).

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