Express as a single logarithm and simplify :

3 log 5 - log 50 + 2 log 2 + 1

Given: 3 log 5 - log 50 + 2 log 2 + 1

= log 5³ - log 50 + log 2² + log 10

= log 125 - log 50 + log 4 + log 10

= log $\dfrac{125 \times 4 \times 10}{50}$

= log $\dfrac{5000}{50}$

= log 100

= log 10²

= 2log 10

= 2

Hence, 3 log 5 - log 50 + 2 log 2 + 1 = 2.