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Chapter 4: Problem 4

For \(x=1.1\) and \(y=5\), evaluate each of the following: (a) \(\ln (x y)\) (b) \((\ln x)(\ln y)\)

Short Answer

Expert verified
For \(x = 1.1\) and \(y = 5\), we find: (a) \(\ln(xy) \approx 1.705\) (b) \((\ln x)(\ln y) \approx 0.153\)

Step by step solution

01

(a) Calculate xy and evaluate \(\ln(xy)\)

First, we need to find the product of x and y: \(xy = (1.1)(5) = 5.5\) Now, we will evaluate the natural logarithm of this product: \(\ln(xy) = \ln(5.5)\) Using a calculator, we can find the numerical value of this expression: \(\ln(5.5) \approx 1.705\)
02

(b) Calculate \(\ln x\) and \(\ln y\) and evaluate \((\ln x)(\ln y)\)

First, evaluate the natural logarithms of x and y: \(\ln x = \ln(1.1)\) \(\ln y = \ln(5)\) Using a calculator for these values: \(\ln(1.1) \approx 0.095\) \(\ln(5) \approx 1.609\) Now, multiply these logarithms: \((\ln x)(\ln y) = (0.095)(1.609)\) Again, using a calculator: \((\ln x)(\ln y) = (0.095)(1.609) \approx 0.153 \)

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