







Differentiate ln[x(2x4)^1/2] 
20140628 

From Igwe: If y=In[x(2x4)^1/2],find dy/dx at x=3 Answered by Penny Nom. 





ln(12 x) = 6 
20110303 

From Carolyn: solve the equation
ln12x = 6
Thank you
Carolyn Answered by Penny Nom. 





Solve e^x + e^(x+1) = 250 
20080825 

From Laura: "solve this equation correct to three decimals"
e^x + e^x+1= 250 Answered by Penny Nom. 





Natural logarithms 
20030722 

From Amanda: I'm going into my senior year of high school. I will be taking AP calculus, and my teacher gave us some homework over the summer. However, there are two things that I do not understand how to do. The first is, she wants us to be able to generate a unit circle by hand using 30, 60 and 90 degree triangles. I have used the unit circle in trigonometry, however I was never taught how to draw it. Secondly, I need to know how to do natural logarithms without a calculator. I was not taught how to do this, and the worksheet I was given only showed me how to complete them using a calculator. Answered by Claude Tardif. 





Radioactive decay 
20000518 

From Catherine Sullivan: Please help me with the following: The radioactive isotope carbon14 is present in small quantities in all life forms, and it is constantly replenished until the organism dies, after which it decays to carbon12 at a rate proportional to the amount of C14 present, with a half life of 5730 years. Suppose C(t) is the amount of C14 at time t.  Find the value of the constant k in the differential equation: C'=kC
 In 1988 3 teams of scientists found that the Shroud of Turin, which was reputed to be the burial cloth of Jesus, contained 91% of the amount of C14 contained in freshly made cloth of the same material. How old is the Shroud according to the data?
Answered by Harley Weston. 





Two calculus problems 
20000501 

From Kaushal Shah: How Do WE Integrate the following Functions,  Integral xtanx dx
 How was natural base "e" discovered and why e=2.7.......
Answered by Claude Tardif. 





Derivatives with logs 
19991026 

From Kate: What is the derivative of 5 to the 5x2 at x equals 0.8? Answered by Harley Weston. 





John Napier and e 
19990206 

From Shimin: I would like to ask about the exact definition of e, its history (like how John Napier came about discovering it) and its applications in problems and real life situations. Thank you! Answered by Chris Fisher. 

