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Chapter 3: Problem 108

Without showing the details, explain how to condense \(\ln x-2 \ln (x+1)\)

Short Answer

Expert verified
The simplified version of the initial expression is \(\ln (x / (x+1)^2)\).

Step by step solution

01

Apply the power rule

Begin by applying the power rule to the second term of the expression. This rule specifies that \(a* \ln b = \ln (b^a)\). In this case, the 'a' value is 2, and 'b' is \(x+1\), so the expression becomes \(\ln x - \ln (x+1)^2\)
02

Apply the subtraction rule

Next, apply the subtraction rule which dictates that \(\ln a - \ln b = \ln (a/b)\). In the current expression, 'a' is 'x', and 'b' is \((x+1)^2\), this leads to a simplified expression of \(\ln (x / (x+1)^2)\)
03

Simplify Further if Possible

In this case, the resulting expression cannot be simplified further. Thus, the final simplified form would be \(\ln (x / (x+1)^2)\)

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