Question

Solve: 1. 1/2log25-2log3+2log6
2. 2-2log5

Answer 1

Assuming log = log10:

1) (1/2) log 25 − 2 log 3 + 2 log 6
= log(25^{1/2}) + 2[log 6 − log 3]
= log 5 + 2 log(6/3)
= log 5 + 2 log 2
= log 5 + log 4
= log 20.

2) 2 − 2 log 5
= log 100 − 2 log 5
= log 100 − log 25
= log(100/25)
= log 4.

Numerically: log 20 ≈ 1.30103, log 4 ≈ 0.60206.