Logs and Inverses

The things on what in understood about logs and inverses were:
1. How to get rid of logs in order to find the variable. Like 7log7^X well the 7 cancels the log7 leaving the x by itself.
2. Also to find the log of a number like log2 32 that is equal to 5. That log is also equal to 2^5=32.
3.Also to extend the log. Like log5(h+d) equals to log5 h + log5 d.
4. Finding the inverse of the log is what is pretty easy most of the times. To find the inverse is just to switch the inputs and outputs.

The things i don't understand:
Mostly i will understand the algebra of the logs and inverses but they are hard when it comes to graphing them. Usually i graphing mess me up when i have to graph the parent function with a new function coming out of the parent function. Then I'm not really sure how to get the new function from the parent function. he the asymptotes to confuse me as well at times.