Natural Log help

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March 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 (:
March 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 $\int_1^c {\frac{{dx}}{x}} = \ln (c)$ .

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

Quote:

Originally Posted by Plato

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

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

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

Quote:

Originally Posted by dondonlouie

wouldn't it just be 1000?

No indeed!

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

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