Problem 98 - Introductory and Intermediate Algebra for College Students 4th

Question

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

Step-by-Step Solution

Answer

The simplified version of \(\ln x-2 \ln (x+1)\) is \(\ln (x/(x+1)^2)\)

Step 1: Applying the Power Rule to the Expression

The first step is to apply the power rule to the expression \(\ln x-2 \ln (x+1)\). This rule gives us the ability to move the coefficient of a logarithm up as its power and transform our expression into \(\ln x-\ln (x+1)^2\)

Step 2: Applying the Quotient Rule to the Expression

Next, you will apply the quotient rule. This rule allows us to combine two logarithms, subtracted from each other, into one by dividing the argument of the first with the argument of the second. As a result, the expression becomes \(\ln (x/(x+1)^2)\)

Step 3: The Final Expression

After applying these properties of logarithms, we arrived at an expression of \(\ln (x/(x+1)^2)\) which is easier to handle than our original one and no further simplification can be done