Question

Express as a single logarithm:
2 + 1/2 log9 − 2 log 5

Answer 1

2 + 1/2 log9 − 2 log 5 = log 12

The expression given is :2 + 1/2 log9 − 2 log 5

We know, log 100 = 2. So, we replace 2 by log 100

log 100 + 1/2 log 9 - 2 log 5

Again, we know, x log a = log (a)ˣ

So, 1/2 log 9 = log (9)^(1/2) = log 3

And, 2 log 5 = log (5)^(2) = log 25

So, the revised expression stands as

log 100 + log 3 - log 25

We know, log a + log b = log ab

So, log 100 + log 3 = log 300

log 300 - log 25

And, log a - log b = log (a/b)

So, log 300 - log 25 = log (300/25) = log 12