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Exponential function

Perlita

New member
Nov 7, 2013
6
Hello everyone,
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
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,779
Hello everyone,
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
Hey Perlita! :)

What you need is that the function is invertible.
And a strictly increasing function is invertible.

To illustrate how it can go wrong when the function is not invertible, consider for instance the function given by $f(x)=x^2$.
We have $(-2)^2 = 4 = 2^2$.
But that does not imply that $-2 = 2$.