







ln(x+3)+ln(x+2)=ln(x+11) 
19991124 

Thibault Portevin pose la question : "Résolvez l'équation : ln(x+3)+ln(x+2)=ln(x+11)" Je suis bloqué, pourriezvous m'aider? Claude Tardif lui répond. 





logarithme neperien 
19991110 

Louise Kieffer pose la question : D'où provient la valeur e ( 2,7....) des logarithmes népériens ? Claude Tardif lui répond. 





y=lnx+(1+ln2)/2 and y=x^2 
20190128 

Mike pose la question : Prove that y=lnx+(1+ln2)/2 and y=x^2 touch each other.
The course is about logarithm and root functions... how should I solve this problem? Penny Nom lui répond. 





Three consecutive natural numbers 
20170611 

Anita pose la question : Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the square of the other two by 60. Find the numbers. Penny Nom lui répond. 





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

Igwe pose la question : If y=In[x(2x4)^1/2],find dy/dx at x=3 Penny Nom lui répond. 





ln(12 x) = 6 
20110303 

Carolyn pose la question : solve the equation
ln12x = 6
Thank you
Carolyn Penny Nom lui répond. 





A Taylor polynomial for (lnx)/x 
20100929 

Dave pose la question : I have a series problem that I cannot solve. The problem asks for you to compute a Taylor polynomial Tn(x) for f(x) = (lnx)/x. I calculated this poly out to T5(x) and attempted to use this to identify a pattern and create a series in order to calculate Tn(x). However, the coefficients on the numerator out to F5prime(x) are as follows: 1, 3, 11, 50, 274... Ok, so the negative is an easy fix > (1)^n1. But the other coefficients are stumping me. I can't see any sort of pattern there and I've tried every trick I know. Is there another way to go about this?
Thanks! Chris Fisher lui répond. 





1/a + 1/b + 1/c < 1 
20100201 

Mrityun pose la question : suppose a,b and c are natural numbers such that 1/a + 1/b + 1/c < 1. Prove that
1/a + 1/b + 1/c < = 41/42. Penny Nom and Claude Tardif lui répond. 





Properties of Natural Numbers 
20090724 

nazrul pose la question : If m,n,k are natural number how can I prove that (m+n)k=mk+nk. In the proof the properties of natural number should be used. Janice Cotcher lui répond. 





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

Laura pose la question : "solve this equation correct to three decimals"
e^x + e^x+1= 250 Penny Nom lui répond. 





Solving with the Natural Log 
20080728 

CB pose la question : I am trying to solve lnx +3ln2 = ln 2/x. Every way I've tried when I go to plug in the solution it doesn't come out right. Penny Nom lui répond. 





0 = (1/t)  [ln(1+r) ln(t)] 
20071018 

Brandi pose la question : Objective: solve for t, where r = 0.05
0 = (1/t)  [ln(1+r) ln(t)] Penny Nom lui répond. 





x= (y/z)ln((1+a^2)/(1a^2)) 
20070926 

John pose la question : If
x= (y/z)ln((1+a^2)/(1a^2))
Please solve for 'a'
Thanks in advance! Penny Nom lui répond. 





Logarithmic differentiation 
20050523 

Richard pose la question : I need to convince myself that I understand the process of
differentiating y=x^{x}.
The specific question is that if I have to take the logarithm of both sides
of the equation how can differentiate the following?
y= {(x+2)^{(x+2)}}/{(x+1)^{(x+1)}}  {(x+1)^{(x+1)}}/(x^{x}),
I have an idea that the differential of this fairly complex function
is itself ... am I right or wrong. Penny Nom lui répond. 





arcsech x 
20050210 

Monica pose la question : Prove that arcsech x = ln[(1 + (1x^{2})^{(1/2)}) / x ] Penny Nom lui répond. 





39 consecutive natural numbers 
20030819 

A student pose la question : Prove that among any 39 consecutive natural numbers it is always possible to find one whose sum of digits is divisible by 11. Penny Nom lui répond. 





Natural logarithms 
20030722 

Amanda pose la question : 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. Claude Tardif lui répond. 





R= 5.3lnx + x. 
20030511 

A student pose la question : Reaction R to a dose x is given by: R= 5.3lnx + x. For a certain drug, R must not exceed 21. Show that a dose between 8 and 12 units satisfies this requirement & find, correct to 5 decimal places, the greates value of x which satisfies this condition? Harley Weston lui répond. 





Subsets of the natural numbers 
20010130 

Christina pose la question : How do I explain why the set of natural numbers (N) cannot be equivalent to one of its finite subsets? Penny Nom lui répond. 





LOG(LN(x)) = 1 
20000728 

An algebra student pose la question : LET F(x)=LOG X AND G(x)= LN X. SOLVE (f *G)(x)= 1 SHOW COMPOSITION AND USE DEFINITION OF LOGS. Harley Weston lui répond. 





Radioactive decay 
20000518 

Catherine Sullivan pose la question : 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?
Harley Weston lui répond. 





Two calculus problems 
20000501 

Kaushal Shah pose la question : How Do WE Integrate the following Functions,  Integral xtanx dx
 How was natural base "e" discovered and why e=2.7.......
Claude Tardif lui répond. 





Natural numbers 
20000412 

Sara pose la question : What is a natural number??? Penny Nom lui répond. 





Capacitor discharge rate 
20000109 

Bill Phillips pose la question : I need to be solve for t in the following rate problem for an electrical capacitor. Vr = E(e^t/RC), e=nat. log 2.718 raised to the t/RC power. Harley Weston lui répond. 





Two derivatives 
19991116 

Gina Renicker pose la question : The derivative of: y=e^{(xlnx)} and y=x^{2arctan(x1/2)} Harley Weston lui répond. 





Derivatives with logs 
19991026 

Kate pose la question : What is the derivative of 5 to the 5x2 at x equals 0.8? Harley Weston lui répond. 





John Napier and e 
19990206 

Shimin pose la question : 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! Chris Fisher lui répond. 

