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. 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 $y=x$.
   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.)