Questions: Simplify 2 ln (x+2)-ln (x+2)-ln (2)-3. ln ((x+2)/2)-3 ln ((x+2)/5) ln ((x+2)/6) ln (x+2)-ln (6) ln (x+2)-ln (5)

Solution Steps

The given expression is:

\[ 2 \ln (x+2) - \ln (x+2) - \ln (2) - 3 \]

First, simplify \(2 \ln (x+2) - \ln (x+2)\):

\[ 2 \ln (x+2) - \ln (x+2) = \ln (x+2) \]

Now, substitute back into the expression:

\[ \ln (x+2) - \ln (2) - 3 \]

Apply the property of logarithms: \(\ln a - \ln b = \ln \left(\frac{a}{b}\right)\):

\[ \ln (x+2) - \ln (2) = \ln \left(\frac{x+2}{2}\right) \]

Substitute back into the expression:

\[ \ln \left(\frac{x+2}{2}\right) - 3 \]

The expression \(\ln \left(\frac{x+2}{2}\right) - 3\) is already simplified.

Final Answer