Question

Value of log(1+2+3) is ​

Answer 1

log 6 = 0.77815125038 ..

Answer 2

Step-by-step explanation:

log(1.2.3)=log1+log2+log3

In word, why is that a log of a series of multiplication of a numbers is equal to the sum of logs of each of the number that its been multiplied before?

So back to your question, say if you do b x bx b then you log the result there, you’ll figure out that the result is equal to

3 x log b=log b+log b+log b

This is due to

3 x log b=log b3=log(b.b.b). Does that make sense to you?

Now, recall the infamous indices property below

ax.ay=ax+y

then we log both side of the equation to get,

log(ax.ay)=log ax+y

log(ax.ay)=(x+y)loga

log(ax.ay)=x log a+y log a

log(ax.ay)=log ax+log ay

Replace ax with p and ay with q we have,

log(p.q)=log p+log q

With a bit of curiosity and creativity it is also true for log(p.q.r)=log p+log q+log r