Question

Evaluate the following:

2 log 2 + 4 log 3 + log 5 – log 7.5 – log 2.16

Answer 1

Given: 2 log 2 + 4 log 3 + log 5 – log 7.5 – log 2.16

Step-wise calculation:

1. Use log rules:

a log x = log x^a

log A + log B = log (AB)

`log A - log B = log (A/B)`

2. 2 log 2 + 4 log 3 + log 5 – log 7.5 – log 2.16

= log (2²) + log (3⁴) + log (5) – log (7.5) – log (2.16) 

= log (4) + log (81) + log (5) – log (7.5) – log (2.16) 

= `log  (4 xx 81 xx 5)/(7.5 xx 2.16)`

3. Compute the product/quotient:

4 × 81 × 5 = 1620

7.5 × 2.16 = 16.2 

So expression

= `log (1620/16.2)`

= log (100)

4. Assuming log = log10 common logarithm

log (100) = 2