### Home > PC > Chapter 5 > Lesson 5.2.2 > Problem5-63

5-63.

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

1. $\log 4 + \log 5 = \log 9$

$4$ and $5$ should be multiplied, not added.

1. $\log_{3} 7 + \log_{3} 7 = \log_{6} 49$

The base should not change.

1. $\log\left(4 · 5\right) = \left(\log 4\right)\left(\log 5\right)$

The log of a product is the SUM of the logs.

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

There is no rule for $\log\left(4 + 5\right)$. Just add them.