Practice!

Sample Problem

Solve ln(x+2)=ln(x+7)-ln(x-1).

x=

Solution

ln(x+2)=ln(x+7)-ln(x-1)

ln(x+2)=ln(x+7/x-1)

x+2=(x+7)/(x-1)

(x+2)(x-1)=(x+7)

x2+x-2=x+7

x2-9=0=(x+3)(x-3)

x=-3, 3

Check for extraneous solutions!

x=-3 is not possible because both ln(x+2) and ln(x-1) are undefined when x=-3.

The only solution is x=3.