# Natural Log help

• Mar 23rd 2011, 01:46 AM
dondonlouie
Natural Log help
I'm stuck on this question;

Suppose c is a number such that area(1/x,1,c)> 1000. Explain why c> 2^1000

can someone clarify what natural log is for me?

thank you so much (:
• Mar 23rd 2011, 02:47 AM
Plato
Quote:

Originally Posted by dondonlouie
I'm stuck on this question;

Suppose c is a number such that area(1/x,1,c)> 1000. Explain why c> 2^1000

I assume by ‘area’ you mean $\displaystyle \int_1^c {\frac{{dx}}{x}} = \ln (c)$.

So you want to solve $\displaystyle \ln(c)>10^3$. Recall that $\displaystyle e^{\ln(c)}=c.$
• Mar 23rd 2011, 04:06 AM
dondonlouie
Quote:

Originally Posted by Plato
I assume by ‘area’ you mean $\displaystyle \int_1^c {\frac{{dx}}{x}} = \ln (c)$.

So you want to solve $\displaystyle \ln(c)>10^3$. Recall that $\displaystyle e^{\ln(c)}=c.$

wouldn't it just be 1000?
• Mar 23rd 2011, 04:10 AM
Plato
Quote:

Originally Posted by dondonlouie
wouldn't it just be 1000?

No indeed!

If $\displaystyle \ln(c)>1000$ then $\displaystyle c>e^{1000}.$