Exercises

1. Solve for x in the equations.

   A)

   
   

   $$\ln(x)+x^x=e$$

   
   

   B)

   
   

   $$\ln(x)+\ln(x+1)=2$$

   
   

   C)

   
   

   $$3^x+2^x=5^x$$

   
   

   D)

   
   

   $$log_{10}(100)=\frac{\sqrt{x}}{7}$$

   
   

2. 
   
   $$f(x)=\frac{e^x-e^{-x}}{e^x+e^{-x}}$$
   
   
   
   
   $$g(x)=\frac{ln(x-2)}{x}$$
   
   

   A)

   Plot the function f on the domain of -10 to 10 and plot the function g on the domain of -1 to 55. Which function is not invertible and why?

   B)

   Find the inverse of the invertible function.

   C)

   Plot the function and its inverse along with the line $y=x$ on the domain of $-3 \leq x \leq 3$.

   D)

   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.)