1. ## H/W Question.

Show that there is a real number x such that cos(x)=ln(x).

Cheers.

2. Originally Posted by ardam
Show that there is a real number x such that cos(x)=ln(x).
If $f(x)=\ln(x)-\cos(x)$ then $f(1)=?~\&~f(\pi)=?$

3. Originally Posted by Plato
If $f(x)=\ln(x)-\cos(x)$ then $f(1)=?~\&~f(\pi)=?$
Then f(1) = -cos(1) = -0.9998476952

And f(pi)= 0.146232736

4. Originally Posted by ardam
Then f(1) = -cos(1) = -0.9998476952

And f(pi)= 0.146232736
Well what does that imply?

5. Originally Posted by Plato
Well what does that imply?
Sorry but im not sure.

Could it be that x is between the values 1 and pi?

6. Originally Posted by ardam
Sorry but im not sure.
What level of mathematics are you doing?
You posted this question in an advanced forum.
You should know the basic tools at this level.

Have you heard of the Intermediate Value Theorem?