Question

Evaluate \[\int\limits_{e}^{4e} 1/x dx\]

Answer 1

do you know the antiderivative of 1/x?

Answer 2

I got this one already \[\ln \left| 4e \right|- \ln \left| e \right|\]
but then I got stuck

Answer 3

use your log rules

Answer 4

\[\log a - \log b = \log\frac{a}{b}\]

Answer 5

I did not learn about it yet

Answer 6

hmm. you should have learned about those before you did calculus. you probably will want to refresh on those. but I gave the formula you need for this question anyways.

Answer 7

we can use ln rule then

Answer 8

oh yeah, I wrote log instead of ln (although it doesn't matter for the rule).

Answer 9

ok...I got it

Answer 10

it works for any logs as long as the base is the same

Answer 11

I'm turning crazy when I took like the whole week for cal..

Answer 12

thank you so much

Answer 13

no worries.

Answer 14

ok

Answer 15

\(\log(4e)-\log(e)=\log(4)+\log(e)-\log(e)=\log(4)\)

Answer 16

Other log rules for you:
\[\Large\log_na+\log_nb=\log_nab\]\[\Large\frac{\log_na}{\log_nb}=\log_ba\]

Answer 17

Super good try on \(\log|4e| - \log|e|\). If we knew nothing of "e", this would be exactly correct. Since we know \(e > 0\), the Absolute Values are not necessary.

Answer 18

You should not be in Calculus without a background in logarithms. Something seriously wrong, there. Find an algebra book - maybe you saved one from a previous class. There will be a section in there on logarithms. Why someone decided to skip the section on logarithms is a grave mystery. Maybe it was assumed that you never would get to the calculus? {shakes head}

Answer 19

Thank you so much tkhunny, I'm planning to review all my math acknowledge on the summer.....