Question

Why is the answer to this equation ln(4)?

Answer 1

calculator?

Answer 2

the problem is \[\int\limits_{e}^{4e} 1/x\]

Answer 3

i know the antiderivative of 1/x is ln(x), correct? but idk where to go from there

Answer 4

evaluate it from those bounds is all
ln(4e)-ln(e)=ln(4)

Answer 5

that's what I thought. I can see with a calculator that ln(4e)-ln(e)=ln(4), but how to I figure that out without a calculator?

Answer 6

\[\int_{e}^{4e}\frac{1}{x}dx=\ln x|_{e}^{4e}=\ln(4e)-\ln e=\ln4+\ln e-\ln e=\ln4\]remember your log rules!\[\log(ab)=\log a+\log b\]

Answer 7

got it! thank you!

Answer 8

welcome :)