Question

Express the following in terms of log 2 and log 3:

log 180

Answer 1

Given: log 180

Step-wise calculation:

1. Factor 180:

180 = 2² × 3² × 5

2. Use log rules:

log 180 = log (2²) + log (3²) + log 5

= 2 log 2 + 2 log 3 + log 5

3. Write log 5 

= `log (10/2)` 

= log 10 – log 2

= 1 – log 2

4. Substitute:

2 log 2 + 2 log 3 + (1 – log 2)

= log 2 + 2 log 3 + 1