### Home > PC3 > Chapter 7 > Lesson 7.2.2 > Problem7-91

7-91.

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)$

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

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

Careful! Look at the bases.

1. $\log(4·5)=$$(\log(4))(\log(5))$

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

1. $\log(4+5)=$$\log(4)+\log(5)$

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