Question

Evaluate the following:

`1/2 log 625 + log 8 - 1/4 log 16`

Answer 1

Given: `1/2 log 625 + log 8 - 1/4 log 16`

Step-wise calculation:

1. `1/2 log 625`

= `log 625^(1/2)`

= log 25

2. `1/4 log 16`

= `log 16^(1/4)`

= log 2

3. So the expression

= log 25 + log 8 – log 2 

= log (25 × 8) – log 2 

= log 200 – log 2

= `log  200/2` 

= log 100

If log means base 10 common log, log 100 = 2.