There is an error in each of the following equations. Explain the error in each case then correct it.  

1. $\log(4)+\log(5)=$$\log(9)$ 

   Hint (a):

   The sum of the logs is the log of the product.

2. $\log_3(7)+\log_3(7)=$$\log_6(49)$ 

   Hint (b):

   Careful! Look at the bases.

3. $\log(4·5)=$$(\log(4))(\log(5))$ 

   Hint (c):

   The log of a product is equal to the sum of the logs of the factors.

4. $\log(4+5)=$$\log(4)+\log(5)$ 

   Hint (d):

   Think about a simple example. $\log(10)=1$
   Does $\log(10+10)=\log(10)+\log(10)$?