Logarithm integral question....

Define the natural logarithm function in terms of the area under the curve y=1/x.
I need some help getting this one started. I also need to explain how to use this definition to find the derivative of y= ln x, and explain how to use the derivative formula from above to prove that ln(a) + ln(b)= ln(ab)... I know it's a lot, but I could really use a push in the right direction. Thank you for the push...

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Originally Posted by bemidjibasser

Define the natural logarithm function in terms of the area under the curve y=1/x.
I need some help getting this one started. I also need to explain how to use this definition to find the derivative of y= ln x, and explain how to use the derivative formula from above to prove that ln(a) + ln(b)= ln(ab)... I know it's a lot, but I could really use a push in the right direction. Thank you for the push...

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The area under a curve f(x) is defined as the integral f(x) dx

If

Then the area under the curve is:





The antiderivative of is

Does that help you get started?

That is a help. Thanks. I will give it a whirl and see what happens... I might need to ask for more help, but I will be able to get a start now.