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Chapter 3: Problem 72

Evaluate \(g(x)=\ln x\) at the indicated value of \(x\) without using a calculator. $$x=e^{-4}$$

Short Answer

Expert verified
The value of the function \( g(x) = \ln x \) at \( x = e^{-4} \) is -4.

Step by step solution

01

Substitute the value of x into the function

Substitute \( x = e^{-4} \) into \( g(x) = \ln x \). This gives \( g(e^{-4}) = \ln(e^{-4}) \).
02

Apply the properties of the logarithm

Make use of the property that \( \ln(a^b) = b \times \ln(a) \). Here, \( a = e \) and \( b = -4 \). This gives \( \ln(e^{-4}) = -4 \times \ln(e) \).
03

Simplify

Because the natural logarithm of e is 1, this simplifies to \( -4 \times 1 = -4 \).

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