Question

5.1. Disprove the statement: If a and b are any two real numbers, then log(ab) = log(a) + log(b).

Answer 1

Answer:

If (a and b )≤ 0 then $log(ab)=log(a)+log(b)$ is disproved

Step-by-step explanation:

If a and b are positive real numbers then:

$log(ab)=log(a)+log(b)$

But if a and b are negative then this axiom is not true as log is not defined

$log_{c}(x)$= undefined   $for \quad x\leq 0$

So if (a and b )≤ 0 then $log_{c}(a)$ and  $log_{c}(b)$ are undefined but $log_{c}(-a*-b)$ is defined.