How to change the expression to a single logarithm

First, you'll use the "Log power rule," which says that . In this case, you're going from the form on the right (with p in front of the log) to the form on the left (with p in the exponent position). So, the expression becomes:



Then, you'll use the "Log product rule," which says that . Again, you're going from the form on the right to the form on the left (basically, from the sum of the logs, to a log of the products). So you get:



There's your expression simplified into a simple logarithm. 

(1/x + 1)^2 + 6 (1/x + 1) +5