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. 
   
   $$f(x)=\frac{ln(x-2)}{x}$$
   
   
   
   
   $$g(x)=\frac{(x+5)^3}{24}+4$$
   
   

   A

   Plot f(x) on the domain $0 \leq x \leq 100$. Plot g(x) on the domain $-15 \leq x\leq 10$. Which function is not invertible and why?

   B

   Find the inverse of the invertible function.(Note, there will be one non-imaginary result, that should be your inverse.)

   C

   Plot the function and its inverse along with the line $y=x$ on the intervals $-5 \leq x \leq 50$ and $-5 \leq y \leq 50$.