Exercises

1. Solve for x in the equations.
   1. $\ln(x)+x^x=e$
   2. $\ln(x)+\ln(x+1)=2$
   3. $$3^x+2^x=5^x$$
   4. $$\log_{10}(100)=\frac{\sqrt{x}}{7}$$
2. 
   
   $$f(x)=\frac{e^x-e^{-x}}{e^x+e^{-x}}$$
   
   
   
   
   $$g(x)=\frac{\ln(x-2)}{x}$$
   
   
   1. Plot the functions on seperate graphs. Which function is not invertible and why?
   2. Find the inverse of the invertible function.
   3. Plot the function and its inverse along with the line $y=x$ on the interval $-3 \leq x \leq 3$.
   4. Show that you have the correct inverse by using the composite definition. (When you come across a simplifying problem and have figured out why the computer won't simplify ask your lab instructor how to bypass this problem.)