Inverses and Logs

Recap 4 major concepts that you have understood about either/both of these two topic

1. I understand how to find the inverse of function. If you are trying to find the inverse of f(x)= 2x+3, then all you will need to do is convert it to an equation, y= 2x+3. Next, get x by itself. This will give you x= y-3/2. Now switch x to f^-1(x) and y to x. This will give you f^-1(x)= x-3/2, the inverse of f(x)= 2x+3.

To verify this, you will need to plug in f^-1(x)= x-3/2 into f(f^1(x)) and f(x)= 2x+3 into f^-1(f(x)). Both should reduce to be x. If not, then it is not the inverse of the function.

2. I understand the concept of "one-to-one." The horizontal line test is used to determine if the graph of a function and its inverse are actually "functions". You do not need the graph of the inverse to be able to do this test, you only need the original graph. If the graph only touches the horizontal line test at one point, then the function is "one-to-one."

3. I understand logarithmic expressions, somewhat. For example, in the expression log416, the base is 4. To solve this problem, you would re-write it as 4^x= 16. Then solve for x. The equation will change to 4^x= 4^2. You can now eliminate the 4 from each side and all you are left with is x= 2.

4. I understand that if you are not given the base in a logarithmic expression, the base is automatically 10. For example, the expression log100 would be re-written as log10100.


Write about what you did NOT understand completely

1. I do not know how to graph logarithms. I couldn't solve the problems #39-42 on page 44. I get confused what to do when there is an "ln."

2. I also get stuck on problems that involve e or ln. For example, in the problem ln(y-1)-ln2=x+lnx, I do not know the final answer should look like or how to simplify completely. I try to solve this problem by first subtracting ln2 from both sides and turning ln(y-1) into loge(y-1). Next, I used one of the log rules to turn ln2+lnx+x into loge(2+x)+x. Then I cancelled loge from both side and got y-1=2+2x. From there I got y=2+3 but I do not know if that is the right answer.