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I was solving this problem:

Justify that ln6= ln2+ln3

So: exp(ln2+ln3)=exp(ln2)*exp(ln3)= 2*3= 6 = exp(ln6)

Till here, my work was okay.

What I didn't understand is : why should we say that the exponential function is strictly increasing over R before being able to simplify the equation and get: ln2+ln3=ln6 ??

Thanks