Log Definition and 632 Threads

I have come across this inequality:$$ g≤ log\ n <g + 1$$ We assume that the base of the log is b >1 and n is all the natural numbers. I would like to know if anyone could provide a proof regarding this and mention for what g ? Is it for all the g which are integers ?

Directions: Use a log table to solve for x: ${2.884}^{x}=0.01439$ $x*\log\left({2.884}\right)=\log\left({0.01439}\right)$ $x=\frac{\log\left({0.01439}\right)}{\log\left({2.884}\right)}$ is the exact answer. The solution to the problem is -4.004 in the back of the book. To evaluate the...

How to write log3 (base 10) in Latex?

Homework Statement Lets say we have a series of balls and an eggs. All items have equal mass but are traveling at different velocities. Thus they have differing kinetic energies. Now, for each 'ball' object we have, we want to find an egg object with a similar kinetic energy. Let's say...

Homework Statement The problem is actually from chemical kinetics, but my problem is solving the differential equation obtained. (dx(t))/(dt) = -j*x^2-k*x+k*a ; x is a function of t, and j,k,a are all real positive constants. Homework Equations I know this is a Ricatti type equation. But this...

Homework Statement If log3(x-3)-log1/3(x+1) is expressed in terms of a logarithm with base 9, then it is equal to? Homework Equations logba=logca/logcb The Attempt at a Solution I know I need to get rid of the 1/2 by multiplying but can't remember how to apply it. log3(x-3)-log1/3...

Hello, I am analysing hydrology data and curve fitting to check the best probability distribution among 8 candidate distribution. (2 and 3 parameter distributions) The selection is based on the lowest AIC value. While doing my calculation in excel, how is it suggested to treat very low (approx...

Homework Statement f(x) = 1/ln (10-x) -- I would assume it to be a fairly simple equation, but I am screwing it upHomework Equations What is f'(x)?The Attempt at a Solution f'(x) = (ln (10-x))^-1 = -(ln (10-x))^-2 * -1 * 1/(10-x) -- 2 negatives cancel out = 1/(10-x) (ln(10-x))2 --...

Homework Statement 1. I have to prove that x+ln(1+e^(-x)) is equal to ln(1+e^(x)) Homework EquationsThe Attempt at a Solution 1. x+ln(1+e^(-x)) =ln(1+e^(x)) ln(e^(-x)+1)+x ln(1/(e^x)+1)+x Im blocked here.. :( thanks

Homework Statement Hello, I had a few derivative of the natural logarithm functions questions. It seems like it should be fairly straightforward, but I am turning it into a pig’s ear.On my honor, none of these are problems on an assessment per se, however, they are not materially different than...

Homework Statement I posted a picture of it and my attempt it is number 3 Homework EquationsThe Attempt at a Solution I tried using log properties and I am not sure what went wrong and how to arrive at the correct answer. Mod note: Messy, disorganized image deleted.

Homework Statement Hello! There is a function in Excel NPER which gives the number of periods/years. Here is the data: Present Value = 7 500 Annual rate 18% Number of periods per year 12 Period rate 0.18/12=0.015 Monthly payment -125 Task to find number of years to pay-off loan with minimum...

If two 5-year survival probabilities are p1=.55 and p2=.41 the ratio is .55/.41 = 1.34 but since probabilities are in [0, 1] should I take the log first? Which is the more appropriate way to interpret the ratio? the ratio of logs is Log(.55)/log(.41) = .671 Which is less than one although...

Homework Statement Hi, I'm new here. I'm really rusty, I resume my career this year, and I'm reading 'the spivak book', (for Calculus 1). Making some exercises, I get curious about how to solve this: x+e^x=4 I would love if someone could give me any trick Homework EquationsThe Attempt at a...

Homework Statement The logarithm of an object changes between days according to a normal distribution with median 0,00065 and std dev 0,0038. Calculate the mean and std dev after 249 days for the real and logarithmic scales. Homework Equations Standard standard deviation as far as I am aware...

Homework Statement Let f(n) denote the number of unique prime factors of some positive integer n > 1. Prove that f(n) \in \mathcal{O}\left(\dfrac{\log n}{\log \log n}\right) Homework EquationsThe Attempt at a Solution Since every prime number except 2 is prime, an upper bound on the number...

Homework Statement I've seen this problem appear in more than one textbook almost without any changes. It goes like this: Assume the entropy ##S## depends on the volume ##\bar{\Omega}## inside the energy shell: ##S(\bar{\Omega})=f(\bar{\Omega})##. Show that from the additivity of ##S## and the...

Using logs to compute the following, to the four-figure accuracy. $\frac{.009292}{(\sqrt[3]{582400}+14.23)}$ Let N=$\frac{.009292}{(\sqrt[3]{582400}+14.23)}$, then $\log\left({N}\right)=\log\left({\frac{.009292}{(\sqrt[3]{582400}+14.23)} }\right)$. Log N=...

Use Logarithms to compute the following, correct to four- accuracy. (In find N from Log N, don't interpolate).26. $$(\log\left({0.007211}\right))^3$$ Let N=$$(\log\left({0.007211}\right))^3$$ Then $\log\left({(\log\left({0.007211}\right))^3}\right)$=$$\log\left({N}\right) $\therefore$...

I was going through some important points give in my textbook and I saw this: ##\log_e x < \sqrt x## How did they get this? I know calculus so you can show this using differentiation, etc. One possible way is that they took ##f(x)=\sqrt x-\log_e x## And tried to prove it is always greater than zero.

Both are logarithms, what is the difference between log and ln?

Hey! :o I am looking at the proof of the following theorem and I have some questions. The theorem is the following: The proof is the following: Let $D(T)$ be the sum of the depths of the leaves of a binary rtee $T$. Let $D(m)$ be the smallest value of $D(T)$ taken over all binary trees $T$...

Hello, I have this problem (warning: log of zero in one function) when i try to simulate one system which apparentely doesn't have any problem. in order to follow with my project i need to know how to change something parameters or whatever that is doing that my equation give me this mistake...

Homework Statement By taking the natural logarithms of each side, that this equation can be linearized by making a semi logarithmic plot. Identify the variables and state what the slope , and y-intercept would represent. Homework Equations F=Fo*e^-(d/cτ) The Attempt at a Solution I tried...

Logarithms N 0 1 2 293 46687 46702 46716 294 46850 46835 46864 295 46982 46997 47012 Prop. Pts 1 1.6 2 3.2 3 4.8 4 6.4 5 8.0 6 9.6 7 11.2 8 12.8 9 14.4 Find the value of $\log\left({29517}\right)$ Work: 4+$\log\left({2.9517}\right)$ Thanks for your help

How can I solve (or evaluating) this integral $$\int_{5}^{\infty}\frac{1}{\log\left(t\right)t^{r}}dt$$ with $r\geq 2$?

Homework Statement Solve for X logx-log(x+11) = -1 and log4x-log4(x+15) = -1 Homework EquationsThe Attempt at a Solution log x - log (x+11) = -1 log (x/x+11) = -1 I don't know how to solve for X after this point log4x-log4(x+15) = -1 log4 x/(x+15) = -1I don't know how to get the X out of...

Does anyone understand how to log linearize, if so how would I go about doing so? Much Thanks

Let k(x) be the curvature of y=ln(x) at x. Find the limit as x approaches to the positive infinity of k(x). At what point does the curve have maximum curvature? You're supposed to parametrize the graph of ln(x), which I found to be x(t)=(t,ln(t)). And you're not allowed to use the formula with...

Homework Statement from -lnIxI to lnI x^-1I , I try to go from -lnIxI to lnI x^-1I by using some properties. Homework Equations - lnIxI The Attempt at a Solution First I write the -lnIxI as -1*lnIxI and then I use -1 as an exponent to absolute value of x in the natural log that is ln (...

A=12^(1/5) Log(A)=(1/5)Log(12) The next part in the book says: Log(A)=0.2158 A=1.644 I don't know how to do this without a calculator, and with a calculator I'm getting 1.24. I'm doing e^0.2158 Can anyone please tell me where I'm going wrong here?Note: this isn't homework, just something...

Homework Statement For example, a linear plot would with x and y values would just plot normally where x and y increases linearly from 0 to infinity. When we use a log graph, do we just plug in x and y to a graph in which the x and y go from 0, 10, 100, 1000, or do we convert the numbers...

Hi, I'd like to know the log properties when they are the power of a constant. I've searched everywhere but I can't find it. the reason I want to know it is that, when solving a recursion tree problem, my teacher got an result of n^(log4 3) but I got 3^(log4 n). the base of the log haven't...

Evaluate the following logarithms, expressing the answers in rectangular form a. $\ln1$, $Ln1$ b. $\ln(3-j4)$, $Ln(3-j4)$ I know that the log of a complex number z is given as $\ln z=\ln|z|+argz$ but I still don't know how to use this fact to solve the problems above. I'm having a hard...

Homework Statement This is not homework, I'd like to know if it is possible to find the pitch a log spiral knowing that at every round (2π) r grows by 535.5 times. For the little I know the equation should be just r = e2π = 535.5 Supposing it starts at r=1cm and goes clockwise, I have...

needed help to solve this math home work? Please help.. What is the value of log(i*pi/2) ? I know the answer is "i*pi/2", but don't know the procedure to solve it. Please help me. Thanks a lot in advance.

The IPCC uses a figure 1.2°C for the direct response to a doubling of CO2, from 280 ppm to 560 ppm. http://www.grida.no/climate/ipcc_tar/wg1/pdf/tar-01.pdf I came up with an equation of 4(log 560)-4(log 280)= 1.2041199. Is this the best way to fit this curve?

Homework Statement If \frac{\log x}{b-c}=\frac{\log y}{c-a}=\frac{\log z}{a-b}, prove that x^{b+c-a}.y^{c+a-b}.z^{a+b-c}=1Homework Equations The Attempt at a Solution I solved a question similar to it in a way. So I tried this in the same way. The only difference between the two questions is...

Does the log property a*log(x)=log(x^a) still hold if a is even and x I imagine that ln(-1)+ln(-1) can't equal zero, even by some mysterious magic involving complex numbers.

Why is e^-1 the inverse of natural log e? Thank you

Hello I have a TI-84 Plus calculator and during my math class we were doing log functions on the calculator and I was met with the err "Argument". I don't know what this means, but from what I've heard my calculator is missing the required software to run a log. I should clarify that when I say...

This is part of a differential equations group project problem where I solve a set of differential equations to obtain the solution to a function. The part that I am stuck at involves taking the log of an exponential function, though there may be a mistake on the book's part, but I'm not sure...

is necessary to simplified the equation before differentiation? could I use the Quotient Rule without of simplifying ?

Here is the code, I am using Mathematica 7 with no packages installed at the moment. $Assumptions = 0 < u <= 19/80 && I10 \[Element] Reals; FXN = Sqrt[(u - 15/16)^2 - 2/5 (u + 17/16) + 1/25] (I10 (u^2) - 1/u); PA = Integrate[FXN /. {I10 -> 1/2 Log[1/2]}, u]; PB = Integrate[FXN, u] /...

Hi all I am using the Kalman Filter with an EM algorithm, (schumway and stoffer). From my understanding the log likelihood should monotonically increase. In some instances however I obtain a decrease in the log likelihood, What can I infer from this? Has anyone experience of these...

I'm trying to solve the product log of (- (3/2) * e ^(3/2) ) as shown in the link below. http://www.wolframalpha.com/input/?i=product+log+of+%28-+%283%2F2%29e^%283%2F2%29%29 This is a complex number of about 1 + 2i. Should I ignore the complex part of the value and is the value (of...

Why is natural log abbreviated as "ln" and not "nl"? I've been taking calculus for a while now and I was just wondering why natural logarithm is abbreviated as "ln" and not "nl". I'm just curious!

Homework Statement Show how 10^(-1.7) = alog(0.3) * 10^(-2) Homework Equations Component: non-fraction part of a logarithm. Mantissa: fraction part of a logarithm. The Attempt at a Solution I'm "reverse engineering" a prof's class through watching his lectures, so I don't have the...

EDIT: my problem is solved, thank you to those who helped Homework Statement Solve: x y^{\prime \prime} = y^{\prime} \log (\frac{y^{\prime}}{x}) Note: This is the first part of an undergraduate applications course in differential equations. We were taught to solve second order...

This thread will be dedicated to find a general formula for the integral I(a,t) = \int^t_0 x \log|\sin(a x )| \, dx \,\,\,\,\, a,t>0 This is not a tutorial . Any comments or attempts are always be welcomed .