Ln Definition and 177 Threads

Homework Statement Let f(x) = ex + ln x Find (f-1) ' (e) Homework Equations let y = f-1 x The Attempt at a Solution I tried finding the inverse of f(x) but got stuck. I arrived at: x = ey + ln y How do I make y the subject of formula?

Homework Statement How do I calculate the variance of \frac{1}{\log{X} + 2} where X is a random variable? The Attempt at a Solution Is it: \frac{1}{\log{var(X)}} Homework Equations The Attempt at a Solution

Homework Statement Determine f^{-1}(0) of f(x) = ln (4-7x) + ln(-7-5x) Homework Equations f(x) = ln (4-7x) + ln(-7-5x)The Attempt at a Solution What I did was y = ln (4-7x)(-7-5x) Then I swapped x and y to attempt to make the inverse function x = ln (4-7y)(-7-5y) and I start to solve...

Is there an easy way to change your y-variable in Gnuplot to ln y without changing the source data file? I already tried "set log y" but that only changed the y-axis scale, not the actual y-values. Right now I'm plotting an exponential decay and I wanted to make it a linear graph (lny vs...

the question is: differentiate wiith repsect to x: (ln(5x))^1/5 i differentiated and got : 1/5ln(5x) y'=1/5x I don't think this is correct. The answer should be ln5/5. Can anyone help me? chanella

How to differentiate y = 8 ln x - 9 x with respect to x^2?

Homework Statement lim(x→∞)(lnx)^2/x Homework Equations The Attempt at a Solution Since lim(x→∞)(lnx )^2=∞ and lim(x→∞)x=∞, the function is indeterminate, ∞/∞. lim(x→∞)(lnx)^2/x=lim(x→∞) d/dx (lnx )^2/(d/dx x)=lim(x→∞)(2 lnx (1/x))/1 An I am stuck...

Homework Statement y=8^0.01x Differentiates to: 0.01 ln8 x 8^0.01x Using derive on a graphics calculator, the answer given is: 3x2^3x-200/100 ln2/25 Prove that the two equal each other using index and logarithm laws. Homework Equations The Attempt at a Solution Ah, well...

Hi, I start with arctanh\left(\frac{A}{\sqrt{A^2-1}}\right)=\frac{1}{2}ln\left( \frac{1+\frac{A}{\sqrt{A^2-1}}}{1-\frac{A}{\sqrt{A^2-1}}}\right) The function \frac{A}{\sqrt{A^2-1}} is real, and since A>1, it too is always greater than 1. Is it true that it should really be the modulus...

Homework Statement Find limit lim x->0+ of lnx+1/x Homework Equations 1/x = ln e^1/x The Attempt at a Solution ln x + ln e^1/x = ln x*e^(1/x) lim x-> 0+ ln x + ln e^1/x = ln 0*inf = ln 0 = - inf lim x-> 0+ Source: my self vs http://www.numberempire.com/limitcalculator.php

I get confused when it is 'ok' to use the natural logarithm when integrating a function. As soon as I see a denominator, I am always tempted to simply go 'ln(denominator)/d denominator)' but this is clearly wrong... Is it wrong in situations where you have a polynomial denominator? For...

Homework Statement Find y' if y = ln( x^2 + y^2 ) Homework Equations d / dx ( lnx ) = 1 / x The Attempt at a Solution y' = ( 1 / ( x^2 + y^2 ) ) * 2x + 2y * y' ( y' / 2x + 2y * y' ) = ( x^2 + y^2 )^-1 I couldn't find a way to isolate y' on its own

Homework Statement I'm trying to understand how they got du in this problem. It is an integration by parts question. Anyway, the question asks me to evaluation this integral by using integration by parts two times Homework Equations This is how we would solve the problem...

Homework Statement I've been going through a book called "Short Calculus: The Original Edition of A First Course in Calculus," by Serge Lang. It says, " The derivative of a^x is a^x (log a)." But everything else I look at says the derivative of a^x is a^x (ln a). Since ln a and log a are...

Homework Statement 2/(x lnx^2) = 1 / (x ln x) That is the answer in the back of my textbook. I have reached 2 ( x ln x^2) , but I do not know why it is = to 1 / ( x ln x ) Homework Equations The Attempt at a Solution I tried to look into precal book to see if I could find...

Homework Statement I'm doing a physics lab and need to do the uncertainties, and the method I'm using is the natural log method, hich goes like this: (equation used was k*(x^a)*(y^b)*(z^c) ) http://img297.imageshack.us/img297/3663/lnform.jpg The equation I'm doing...

Homework Statement Find dy/dx of y=1/xlnx Homework Equations I thought that I'd have to use the quotient rule: y'=vu'-uv'/v^2 However the differential of 1 is 0, so is this the right rule to use? The Attempt at a Solution u=1 u'=0 v=xlnx v'=1/x y'=vu'-uv'/v^2...

Homework Statement Find lim_{n \rightarrow \infty} \sqrt[n]{n ln(n)}. Do not use L'Hospital's Rule or Taylor Series. Homework Equations The Attempt at a Solution I suspect I need to set up some inequality for this and then apply Squeeze Theorem. But I can't find any inequality...

1. Plot f(x)=5+ln(-2x+3), and its inverse. 2. I know the inverse of ln(x) is exp(1)^(x)., and to find the inverse of a function, solve for x then swap the x and y. 3. y=5+ln(-2x+3) y-5=ln(-2x+3) exp(1)^(y-5)=(-2x+3) (-1/2)*[exp(1)^(y-5)-3]=x...

Can somebody show a step by step process of how to get this answer? I keep getting -∞ when it should be ∞ heres my work: lim x→∞ (x - ln x) = lim x→∞ ((1 - 1/x ln x) / (1/x) then apply l'hospitals rule lim x→∞ (x^(-2) ln x - x^(-2)) / (-x^(-2)) then I cancel all the x^(-2) and...

Homework Statement hey guys, got a question. how do you differentiate y=ln(1+x^2)^1/2. any help would be appreciated, thanks Homework Equations answer is x/(1+x^2) The Attempt at a Solution

hello, I was trying to figure out what will be the y value for this equations: 1 - e^-0.15*10^-5*y = 0.1 Could somebody help me in this?? The answer is supposed to be 70,240. thanks.

Homework Statement lim as x approaches 0 of (x + 1)ln x Homework Equations The Attempt at a Solution I tried using ln y = (ln x)[ln (x + 1)] then: ln (x + 1) ---------- 1 --- ln x to make it eligible for L'Hopital's Rule. Then differentiating the numerator and the denominator, I got: 1 --- x...

How do you integrate (ln ln x)^n for any n?

as part of a question i need to integrate \intln2|x|dx (from -1 to 1) what i did was integration in parts \intln2|x|dx =x*ln2|x| - \int2(lnx/x)xdx =x*ln2|x| - 2[xln|x| - x] =lim x(ln2|x|-2ln|x|+ 2)|^{-1}_{0-\epsilon} +(ln2|x|-2ln|x|+ 2)|^{0+\epsilon}_{1} \epsilon->0 1st of...

I don't understand what is happening in the following problem. What happens to ln when it moves to the RHS? Why are there two exponential functions on the RHS and why is e^c made to equal A? http://users.on.net/~rohanlal/mathproblemln.jpg

Homework Statement Differentiate the following: y = ln(2x^2 - 2) / x^2 - 1 The Attempt at a Solution The answer is y' = -ln(2x^2 - 2)(2x)(x^2 - 1)^-2 + 4x / 2x^2 - 2 (x^2 - 1)^-1 I understand all of it except 4x / 2x^2 - 2, how does ln(2x^2 - 2) derive into 4x / 2x^2 - 2?

Homework Statement http://img5.imageshack.us/img5/2327/nummer1.jpg Homework Equations 5a: ln((x*(x-2))/(x2-4)) ln((x22x)/(x2-4)) ln(x/(x+2)) <-- the answer (i think) The Attempt at a Solution Im not completely sure about that answer in 5a so could somebody check...

Homework Statement http://img16.imageshack.us/img16/2327/nummer1.jpg Homework Equations Sn=(u1(rn-1))/(r-1) The Attempt at a Solution I think i need to use the equation for geometric series(above). Or do i use the arithmetic furmula since ln(a/b)=ln(a)-ln(b). I think i am a bit...

\lim_{x->3^-} ln^2(9-x^2)=+\infty the meaning of this ln is e^+infinity=closser to 0 how is that?? by my math e^+infinity is infinity

2x^3lnx+x^2-4x+a=0 i thought of building a taylor series around 0 for ln but ln(0) is undefined ??

find the solution of this ln equation: ax=lnx i tried: e^{(ax)}=x e^{(ax)}-x=0 what to do next?? i thought of building a taylor series around 0 for ln but ln(0) is undefined ??

Homework Statement If a differentiable function f(x) satisfies the equation f(xy) = f(x) + f(y), prove then that f(x) = alnx. Homework Equations The Attempt at a Solution I have proved that if f satisfies f(x + y) = f(x)f(y) then f(x) = 0 or f(x) = e^(ax) and I also know that...

I am completely at a loss with this question :confused: If one assumes that the current growth rate of consumption remains constant, the then expiration time in years is give by: T=1/r ln (rR/C + 1) where C = current consumption, r = current growth rate of consumption, and R = resource size...

Homework Statement Int(x^2-3x+2)/(x+1)dx Homework Equations The Attempt at a Solution I don't know where to start.

I am having trouble generating a MacLaurin Series for ln (1+x^2) Please help me out on this.

In calc we are having like this flash card quiz and you have to apply things to the graph of like e^x or lnx. I was wondering how do you determine the domain range of graphs like these. for example e^x graph domain is all reals, and the range is 0 to infinity. How would you transform this...

is it possible to simplify this more?? Ln(log7-log76)= Ln(log77)

I have tried quite a few methods but haven't solved this problem, any help ? \oint axLn(x/b) dx where a and b are constants I have tried moving the 'a' outside the integration and solving xln(x/b) using integration by parts . I have also tried splitting xln(x/b) into xlnx -xlnb and...

Homework Statement I'm taking a math of investment and credit course, in this case, solving for i which is the interest rate. My question is: is it possible to "ln both sides" of an equation? Like in (b) below, I know I could say y*ln(1+i) = ln(3). Homework Equations (a) 5(1+i)^8 +...

Homework Statement limit x --> infinity, (1+ [(ln2)/x])^x Homework Equations The Attempt at a Solution I tried raising the whole thing to e ln [function] so that the x power would get eliminated. What I've got right now is this: e lim(x->infinity) ln([x+ln2]/2)^x e...

Homework Statement Hi. I'm having problems with the limit of x --> 1 of ( x / ln(x) ). Homework Equations L'Hopital's Rule Algebraic Manipulation The Attempt at a Solution I understand that the the limit will give me a semi-indeterminate form (that is, it's answer is 1 / 0)...

1. lnx + ln(x+2) = ln3 2. just work the problem out using distributive property [b]3. ln2x = ln3-ln2 ln2x = .4054/b] ehh..I am just doing this one wrong. It is hard to believe what summer vacation can do to you :redface:

I have to sketch the following function: y=x(lnx)^3 The ln scares me a bit... I have found the derivative of the function as 3(lnx)^2, and when making that equal to zero I got an anwer of around 0.7 if i remember correctly. This I guess is my critical number? Then the second derivative is...

Homework Statement Find \int ln x^{2009} Homework Equations The integration by parts! The Attempt at a Solution I have been trying to discover a series which might have helped: I have taken out the integrals of : 1) ln x = x ln x -x 2) ln x^{2}=x (ln x^{2})-2x ln x +2x 3)ln...

hi, I'm new around here but i really need your help this question is similar to one already solved here some years ago so my problem is: 1.The vapour pressure of benzene between 10°C and 30°C fits the expression log(p/Torr) = 7.960 - 1780/(T/K). Calculate (a) the enthalpy of...

Can anybody recommend a good site to bone up on differentiating and integrating ln and e functions?

f(x)=x^3lnx^2 product rule y'=u'v+v'u u=x^3 u'=3x^2 v=lnx^2 v'=2lnx^2 f'(x)=3x^2(lnx^2)+2x^3lnx^2) but answer in book is f'(x)=3x^2(lnx^2)+2x^2 What am i doing wrong?

Can someone explain how the integration of 1/x = ln x I understand the usual way results in division by zero and that the derivative of ln x = 1/x So my question is, how is the quantity of area under the curve from 1 to x relate to the natural log of x

I am not sure how would I work this problem. Any help would be appreciated. Estimate ln 1. 5 = Integral from 1 to 1.5 dt/t using the approximation 1 2 [Lf (P) + Uf (P)] with P = {1 =8/8, 9/8, 10/8, 11/8, 12/8=1.5}