Question

Evaluate the following:

log 5 + 3 log 2 – 2 log 6 + 2 log 3

Answer 1

Given: log 5 + 3 log 2 – 2 log 6 + 2 log 3

Step-wise calculation:

1. Apply the power rule:

3 log 2

= log (2³) 

= log 8

2 log 3 

= log (3²)

= log 9

2 log 6 

= log (6²) 

= log 36

2. Substitute:

log 5 + log 8 – log 36 + log 9

3. Combine using product/quotient rules:

`log(5 xx 8 xx 9)/36`

= `log(360/36)`

= log 10

4. For common logarithm base 10

log 10 = 1