Taking log on inequality

Question

I have an inequality

$a\geq b + c$

where $a,b$ and $c$ are positive numbers.

Can I write this in the following way?

$log(a) \geq log(b) + log(c)$

Answer 1

$a=5,b=2,c=3$ is a counterexample.

Answer 2

No, you can't write. As, $\log(a+b) \not= \log(a) +\log(b) $(in general).

Only, $\log(ab) = \log(a)+\log(b)$

Answer 3

Hint: Log is a monotonous function and so $a\geq b$ implies $\log a \geq \log b$. But $\log (b+c)\ne \log b+\log c$. Its $\log (bc) = \log (b)+\log(c)$.