H/W Question.

**ardam** · November 19th 2009, 10:26 AM

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

Cheers.

**Plato** · November 19th 2009, 10:57 AM

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 $f(1)=?~\&~f(\pi)=?$

**ardam** · November 19th 2009, 12:36 PM

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

**Plato** · November 19th 2009, 12:41 PM

Originally Posted by ardam

Then f(1) = -cos(1) = -0.9998476952

And f(pi)= 0.146232736

Well what does that imply?

**ardam** · November 19th 2009, 01:31 PM

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?

**Plato** · November 19th 2009, 01:36 PM

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?

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