Logarithm Definition and 335 Threads

Does anyone know if the property of the logarithm function that: log(ab)=log(a)+log(b) is unique to that function? In other words, has it been shown that there can be no other function with that property? -j

Well I came across this when someone asked me this question: (-2)^n = 16 I can clearly see n=4. However, he did this: ln((-2)^n) = ln(16) n*ln(-2) = ln(16) n*ln(2)+n*i*pi = ln(16) How can I show that n=4 from this?

Hi everyone. I know this question is quite simple but I can't wrap my head around it at the moment.. Solve for y: ln(x) + ln(y) = 0 I've tried differentiating both terms and then arranging for y but I get y = -x. The answer is meant to be y = 1/x. Thanks all!

Hi, Okay, I just went over some old stuff this week to prepare for the next vast vast, upcoming test. I came across a Logarithmic Equation book, well, it's more than 300 pages long, it covers most things from Exponential to Logarithm. :woot: I have read about 1/4 of it, and I was stuck...

Homework Statement Given that \log_{4n} 40\sqrt {3} = \log_{3n} 45 find n^3 Homework Equations Logarithm properties The Attempt at a Solution I can get an expression for n but looks messy, and suspect there is probably a more compact answer. This is what I did...

Hello everyone, I do not understand how:: e raised to ln of x = x ? this notation might make more sense:: e^ln x=x ? Thanks for the help.

Homework Statement xln(2x+1)-x+\frac{1}{2}ln(2x+1) = \frac{1}{2}(2x+1)ln(2x+1)-xHomework Equations ln(x^a) = aln(x), ln(xy) = ln(x) + ln(y), ln(\frac{x}{y}) = ln(x) - ln(y)The Attempt at a Solution I have no idea how you can go from xln(2x+1)-x+\frac{1}{2}ln(2x+1) to...

Actually, I am trying to use what I have learned on school to something else Homework Statement 3*10^x = 1.73*10^14 Homework Equations lga^x = xlga The Attempt at a Solution 10^x = (1.73 * 10^14)/3 10^x = 5.767 * 10^13 xlg10 = 13lg(57.67) x=13lg(57.67) x=22.89 :\...

Homework Statement Show that ln(z^\alpha) = \alpha ln(z) where 'z' and 'alpha' are complex. Homework Equations ln \alpha = ln r + i(\theta + 2*n*\pi) The Attempt at a Solution For the left hand side I have ln (z^\alpha) = ln...

Hey! I have always learned that functions like logarithms, exponentials, trigonometrics etc. have to operatore on pure numbers and not numbers with units. For instance, you cannot write: Sin ( 5 kg*m/s^2 ) But in chemistry I often find formulas where logarithmes of numbers with units...

Hi all, I'm a bit puzzled by one of my homework questions. I got an answer, but I have nothing to check it with and I'm not sure that my answer is correct. The question states that y=ln(ln(ln(x))), and asks for y'. This is what I've done, but it seems a bit too simple to me...

Can't start: (log_{a}b)(log_{b}a) =1

log2 2x -log3 (3x-1) = 2, solve for x... you guys don't hv 2 solve the question for me, just guide me to the answer:smile:

I was doing some assignment i have to give in, for math, and came upon this exponential equation: (2^x+1) + (2^x+2) = (2^1-x) + (2^3-x) I thought, pfft, that's easy...so i did it, wrong answer, tried something else, wrong answer..tried another tactic, and i think you can guess what...

I need help defining a logarithm. My book simply says: A logarithm is an exponent. This stumped me because I can't see how that is. I don't know what question to ask, but I might not be apprehending the relationship between an expo. function and a log. function.

#2 Hi, Well can anyone tell me how to find the natural logarithm of a complex number p + iq. Also please tell me how to convert it into logarithm to the base 10. An external link to a webpage (where all the details are given) will be appreciated.

Confused, but tried it this way: Use u-substitution to show that (for y a positive number and x>0) \int_{x}^{xy} \frac{1}{t} dt = \int_{1}^{y} \frac{1}{t} dt so, u=t and du=dt if x=1 t=xy u=y(1)=y t=x u=1 or u=1/t and du/ln [t] = dt if x=1 t=xy u=1/y t=x y=1 Thanks for...

The question is this: Consider p(z) a polynomial and C a closed path containing all the zeroes of p in its interior. Compute \frac{1}{2\pi i}\int_C z\frac{p'(z)}{p(z)}dz The solution given by the manual starts by saying that \frac{p'(z)}{p(z)}=(log(p(z)))'. But there is no...

my physics teacher told us that for now well be solving the equation of a line such as y=kx^n by trial and error for finding "n" using the multiplicative change in 2 points i.e x_1,y_1,x_2,y_2. what we would do is for example 2 points (13,1) (6, 1.4): n=\frac{y_2}{y_1}=(\frac{x_2}{x_1})^n...

Hello sorry to post another so soon. This book is VERY hard to learn from... its not very good at explaining. The question says: Evaluate the following logarithm: 10log1019. It never showed me how to do it when there's a number in front of the log. What I got from the log 1019 is...

I haven't been able to prove: ln(e)/e > ln(pi)/pi without calculating any of the values. Help would be much appreciated.

hi could anyone tell me where I went wrong ? simultaneously solve 2logbase2 y = logbase4 3 + logbase2 x 3^y = 9^x But for the top I get y = 3 root x and bottom I get y=3x so what's gone wrong ? thanks roger

I don't know how to show that: 2/log underscore9 A-1/log underscore3 A = 3/log underscore3 A

I'm puzzled by... \ln \left( -\frac{1}{2} \right) = - \ln \left( 2 \right) + i \pi Why is this true? How can I possibly get this result? I know that \ln \left( \frac{1}{2} \right) = - \ln \left( 2 \right). Thank you so much

Is it true that that ln(-x) is defined for x \in R such that x < 0? - Kamataat

My book have a really crappy proof of how log a^x = x log a can be true. Can someone help me? Another question deals with an application of it which made me really confused: Factorise (4a^3) - (29 a^2) + 47a - 10 then solve (4*4^3x) - (29*4^2x) + 47*4^x - 10 = 0 I see...

Hey I am doing an investigation for logarithms, and I have a question. logx^n = nlogx. Based on previous knowledge of exponents, could someone please explain why this is true? Thanks.

I need to solve 7^2x - 5*7^x - 24 =0. Am I on the right track by starting with 7^2x - 35^x - 24 = 0?

I'm trying to use LOGs other than log base 10 and base e on my TI-86. Can I accomplish this like this?: log base a of b = (log base 10 of b) / (log base 10 of a) ? or is it: log base a of b = (ln b) / (ln a) ? Help needed ASAP. Thanks!

I've just introduced myself to logarithms and have done most of the questions, but am having trouble with one or two of them: Q1: Find values of x for which: Log(to base 3)x - 2log(to base x)3 = 1. I have no idea where to start on this question. Q2: Solve: 25^x = 5^(x+1) -6. On...

I have a small problem with logarithms. We have to solve physics and chemistry problems using only logs. And I don't know how to do the following - 1.2341 + bar2.4412 Well actually my question is how do you add or subtract bar numbers ? (It's the numbers with '-' on top) Rohit.

What I have not seen in books about the Gibbs paradox is that it doesn't exist if we make the Gibbs correction at the logarithm of the Z function, not at the Z function itself, in that way: \ln Z_{i} - \ln N_{i} ! where N_{i} is the number of identical particles of class i, where there...

can some one explain to me how is taking the logarithm of euler product gives you -sum(p)[log(1-p^s)]+log(s-1)=log[(s-1)z(s)]? my question is coming after encoutering this equation in this text in page number 2...

log_10x-2=0 ... that's log base 10 (answer: 100) ln(x+5)=ln(x-1)-ln(x+1) (answer: no solution. but why?) log_4x-log_4(x-1)=1/2 (answer: 2)

Their must be over a million definitions involving the constant "e". What I would like is a description of the natural logarithm in natural terms, not just saying "e is where e [inte] dx/x=1, etc." 1 In other words, why choose this function to define e, and how does it most...