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.(To decide which is the correct answer go ahead and plot them).
   3. Plot the function and its inverse along with the line $y=x$ on the intervals $-3 \leq x \leq 3$ and $-3 \leq y \leq 3$.
   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.)