Questions related to real and complex logarithms.

learn more… | top users | synonyms

0
votes
1answer
47 views

Logarithmic Equations: Solving for the unknown variable

What is $y$ in $$3^{2y}\cdot3^{\log_{3}(1/3)}=9$$ I apologize if this is confusing, i wasn't sure how to type this equation in here to ask it. If you can please show the steps it would help me ...
0
votes
2answers
21 views

Taking the logarithm of both sides of $x=(ab/b)^y$

I got confused at $x=(\frac{ab}{b})^y$. If you take the logarithm with base $b$ of $x=(\frac{ab}{b})^y$, wouldn't it be $y\log{bx}=\frac{ab}{b}$. Why did the solution suddenly take the log of ...
0
votes
0answers
28 views

Is this basic proof complete?

I have a problem with proving that the limit as x goes to infinity for lnx/x is 0. Take the most basic approach: Note that the derivative of lnx is 1/x whereas x has a derivative of 1. Hence, lnx is ...
0
votes
1answer
30 views

Change base log formula?

Im trying to change the base log from ln to log with the following formula. y = a * ln⁡(x+c) + b The ln equation is: ...
3
votes
1answer
43 views

Show that any invertible matrix has a logarithm.

I was trying to remember how to show that any invertible matrix has a (possibly complex) logarithm. I thought what I came up with was kind of cool, so I thought I'd post my answer here.
0
votes
3answers
49 views

How do you solve a equation by converting to logarithm form for the problem$3e^{x-4} +2=83$?

$3e^{x-4} +2=83$ I understand converting logarithms but i dont understand how to convert e into log form and solve. help would be deeply appreciated.
1
vote
2answers
65 views

Conformal Mapping Between Two Domains (log)

Does anyone have a recommendation as how to go about solving this problem? I want a conformal from G to H where $$ G = \{ z \in \Bbb C \ | \ |z|<1, |z+i|>\sqrt{2} \}, S = \{ z \in \Bbb C \ | \ ...
0
votes
2answers
32 views

How to substitute $\log_{10}$ for $\ln$ function?

Im wondering how I could go about substituting $\log_{10}$ for $\ln$ in the following formula? $y=a+b\ln(x+c)$ Is there a simple way of doing this? Cheers
0
votes
2answers
33 views

How can i solve limit.

Hello I have a silly question: How can i show that $\lim\limits_{x \to \infty} \dfrac{\log(x+1)}{\log{x}}=1$. Thank you.
0
votes
2answers
92 views

A definite integral involve Logarithmic Functions

Here is the integral body: $$\int_0^m {{x^a}\ln \left( {x + b} \right)dx,a > - \frac{3}{2},b > 0} $$
1
vote
3answers
130 views

Convergence of series minus logarithm

im trying to solve this problem since two, three days.. Is there someone who can help me to solve this problem step by step. I really want to understand & solve this! $$ Show\ \exists \ \beta ...
3
votes
0answers
42 views

Exercise concerning logarithms…

I have such a problem: find all the values of real parameter "a", for which the following inequality is true for any "x" that belongs to R. I will show you my solution, and please can you verify ...
1
vote
0answers
35 views

Finding the $\log$ of a matrix by contour integration

My teacher presented this way of determining the logarithm of a matrix $\Omega$ in class today: $$\log \Omega = \frac1{2\pi i}\oint_{\Gamma} (\zeta I - \Omega)^{-1} \log \zeta \,d\zeta.$$ Does ...
0
votes
2answers
48 views

Logarithm problems with different bases

$ \log_a{b} \times \log_b{a} = $ ? $ \log_a{b} + \log_b{a} = \sqrt{29} $ What is $ \log_a{b} - \log_b{a} = $ ? 3. What is b in the following: $$ \log_b{3} + \log_b{11} + \log_b{61} = 1 $$ and ...
1
vote
1answer
26 views

I can't find second solution to this logarithmic problem!

I kind of got stuck on one step in solving a logarithmic equation. The equation given was: x^3lnx - 4xlnx = 0 My steps so far: x^3lnx - 4xlnx = 0 ln((x^x^3)/(x^4x)) = 0 e^ln((x^x^3)/(x^4x)) = ...
1
vote
2answers
28 views

How do I find the inverse of this exponential function?

$x=-3(3^{-x})+9$ I know the steps up until a certain point. $x=-3(3^{-y})+9$ $x-9=-3(3^{-y})$ $\frac{(x-9)}{-3} = 3^y$ $ln (\frac{x-9}{-3}) = -y * ln 3$ Not sure what to do from here. I know I ...
1
vote
1answer
25 views

Name for property?

This may be a stupid question, it may not. But I was working on some basic logarithm problems and found out that: $-\log(a/b)=\log(b/a)$ Is there a name for this property? Here's my proof: ...
1
vote
0answers
50 views

Is $\log^* (n+1)^{n+2} \in O(\log^* n)$?

I would like to know if $\log^* (n+1)^{n+2} \in O(\log^* n)$, where $\log^*$ is the iterated logarithm. I tried doing: $ \log^* (n+1)^{n+2} =\\ \log^{*}(\log(n+1)^{n+2})-1 =\\ \log^{*}((n+2) \cdot ...
0
votes
0answers
30 views

Summation of a function with the variable both in the function amd in the upper limit

E is defined as : E = c1 ( a$\rho$ + b$\rho ^{2}$ ) + c2 $\rho$ ( c + d $\sum_{j=0}^{n} (\log{ \frac{R\rho}{j} } ) $ ) + c3 $\rho ^{2}$ a, b, c, d, c1, c2, c3, R are known constants. $\rho$ is the ...
0
votes
2answers
112 views

Is this a logarithmic spiral?

I'm trying to draw a logarithmic spiral by hand (actually I need to use a plotter to cut a spiral on wood, but that is another story) and I saw this method: ...
0
votes
1answer
47 views

(log n)^k = O(n)? For k greater 1

$$(\log n)^k = O(n)?$$ For $k> 1$. $k$ is a constant, such as number $4$. I think it is not true for $n=32$ and greater. $n=32, n=64, n=128,\dots$ So, I can not find $n_0$ and $c$.
0
votes
1answer
32 views

natural log notation $\ln^{10}k$

I have a question about some notation I came across in my math text book. I've never seen this before so I'm not sure what it means. The problem is to use the divergence test to show that an ...
0
votes
5answers
68 views

Show $(\ln(x^2))^2-(\ln x)^2=3(\ln x)^2$

I read an example on integrals. I can't see how $$(\ln(x^2))^2-(\ln x)^2=3(\ln x)^2.$$
1
vote
0answers
44 views

Why doesn't Logz/z have zeros?

Our book claims that $\frac {Logz}{z}$ has no zeros, where Logz is the principle branch of the complex natural logarithm. However, $Logz=log|z|+iArg(z)$, correct? So $Log1=log|1|+iArg(1)=0+i0=0.$ ...
1
vote
1answer
32 views

Confused about discrete logarithm question

For purposes of explaining the notation for those unfamiliar, if we fix a prime $q$, as well as $a,b$ nonzero integers $\mod{q}$, $L_a(b) = x$ is the solution to the equation $b = a^x \mod{p}$ We are ...
2
votes
1answer
67 views

Separating the log of a sum

I know there is no formula to separate the log of a sum, e.g. $\log(X+Y)$ into two parts, but are there any approximation rules that can allow me to achieve this objective? ...
0
votes
1answer
36 views

Prove this logarithm equation

I keep getting the wrong answer. Can someone please correct my working out a^x=b^(1-x) In(a)^x=In(b)^(1-x) xIn(a)=(1-x)In(b) xIn(a)=In(e)-xIn(b) xIn(a)+xIn(b)=In(e) x[In(a)+In(b)]=Ine ...
2
votes
2answers
62 views

Limit of a Logarithm with Different Bases

We are to compute $$\lim_{n->\infty}{\frac{2^{\log_3 n}}{3^{\log_2 n}}}$$ Clearly the bases are reversed between the logarithm and exponents, so I can't seem to find any logarithm or exponential ...
0
votes
1answer
47 views

Inverse Function of Logarithm

The answer is A but I don't understand why! $ -2 \log_e (x^2) $ can be re-written as $ -4 \log_e(x) $ right? but why do these two graphs look different? the graph $-2 \log_e (x^2) $ is one to ...
0
votes
1answer
19 views

Maximum value of constant in logarithm problem

The first thing I did was: make: (x-1)^2 - k > 0 (x-1)^2 > k don't know what to do after this point... the maximum value of k is 9 i dont really understand what the maximum value of k is? ...
1
vote
1answer
48 views

weighted average with exponential weighting

I want to create weighted average, where weights depend on value of number. If I want exponential weights is this regular? $average = \log_e(\frac{\sum_{i=1}^n e^{v_i}}{n})$ Isn't it just average of ...
1
vote
0answers
36 views

Interchanging from exponential form to log form

Shouldn't the answer be x = loge(everything else in the bracket) why is the loge function divided by "k" ???
3
votes
2answers
119 views

How to find $\int_2^x t/(\log t)^2 \,dt$

$$\int_2^x \frac{t}{(\log t)^2} \,dt,$$ I want to write this integral with $Li(x)$ or $Li_2(x)$. How can i do that?
0
votes
3answers
93 views

Solution to $x=100e^{-x/100}$?

How do you solve $$x=100e^{-x/100}$$ If I use $\ln$ then $\ln(x/100)=-x/100$. How do I get from that to $x=56.7$?
1
vote
1answer
26 views

Help with integral/logarithm inequality

I have to prove the following inequality: $1/(n+1) < \int_n^{n+1} 1/t$ $dt$ $<1/n$ I thought it would be easier to attack this via integration, so I get: $1/(n+1) <$ log $(n+1)-$ ...
1
vote
3answers
33 views

A question on Logarithms

Q: Given that $\log_3(x) = a$ solve for $x$, $\log_3(9x) + \log_3(\frac{x^3}{81}) = 3$ \I make progress by writing $\log_3(9x) = 3^{2+a}$ and $\log_3(\frac{x^3}{81}) = 5a - 4$. However, I can't ...
2
votes
0answers
38 views

When this inequality true?

If $a$ and $b$ are non-negative integers and $c$ and $d$ are non-negative real numbers, for what values is the following inequality true? $\log((a+b)!) - \log(a!b!) \ge(a+b) \log(c+d) - (a \log(c) ...
2
votes
1answer
37 views

How to evaluate square of logarithms to solve s(n) = O(a(n))?

I've never used log before, nor worked with big-O notation, so I'm completely useless at this stuff. Any, any, any help or direction you can give would be helpful as the professor hasn't covered this ...
2
votes
2answers
94 views

Find the order of magnitude of the equation solution

Find the order of magnitude of the following equation solution: $$ x(\ln x)^{2001}=n $$
0
votes
1answer
17 views

clarification on logarithm problem

I was wondering if someone could explain what is going on in this problem. I understand that it makes sense that $(x = 0)$ I'm not sure why $(x<0)$ or $(x>0)$ are ruled out. LS and RS mean ...
4
votes
5answers
135 views

Calculate ln(x) using 8-digit calculator

I have a bit of a unique problem. Well, maybe not a problem because I'm really just curious about it, but... I have a simple 8 digit calculator. It has +, -, x, /, and a constant operation function. ...
3
votes
2answers
22 views

Patrial Fraction definite integral with non-real part

I have a question to find the area bounded by $y = \dfrac{x^2-4x-4}{x^2-4x-5}$ and the x-axis. First I found the bounds by solving where the numerator would equal zero. My result is $2\pm2\sqrt2$ so ...
0
votes
1answer
41 views

Relationship between logarithms and harmonic series

This article on the harmonic series says that $$\sum_{n=1}^k\,\frac{1}{n} \;=\; \ln k + \gamma + \varepsilon_k$$ where $$\varepsilon_k\sim\frac{1}{2k}$$ and this seems to generalise to ...
1
vote
1answer
80 views

Explicit proof of the derivative of a matrix logarithm

Firstly, I'm but a mere physicist, so please be gentle :-) I want to explicitly show that the derivative of the (natural) logaritm of a general $n \times n$ (diagonalizable) matrix $X(x)$ w.r.t. $x$ ...
1
vote
1answer
26 views

Sketching Logs with Quadratic Terms

$\log(x^2+1) = y$ asymptote at $x^2+1 > 0$ and so there is no asymptote $x$ and $y$ intercept at $(0,0)$ How do you know that the function goes both directions, and has a dip in the middle? ...
5
votes
4answers
348 views

What are logarithms?

I have heard of logarithms, and done very little research at all. From that little bit of research I found out its in algebra 2. Sadly to say, I'm going into 9th grade, but yet I'm learning ...
0
votes
1answer
33 views

Taylor Expansion and Log transformation (Time Series)

From: Time Series Analysis with Applications in R by Jonathan D. Cryer and Kung-Sik Chan. Here is the Taylor expansion: $\log Y_t = \sum_{n = 1}^{\infty} (-1)^{n+1} \frac{(Y_t - 1)^n}{n} $. How ...
6
votes
2answers
712 views

Product of logarithms, prove this identity.

Is it hard to prove this identity: $$2 \log (a) \log (b)=\log(a b)^2-\log(a)^2-\log(b)^2$$ for $a>1$ and $b>1$?
1
vote
3answers
95 views

Evaluate the integral. $\int x^2 \log(4x) dx$

The problem is $\int x^2 \log(4x) dx$ Here $\ln$ refers to the natural logarithm. So far, I know $u = x^2$ and $du = 2x (dx)$. So $dv = \ln(4x) dx$ and $v = 1/x$, but I don't know where to go from ...
3
votes
3answers
168 views

Solving ${\sqrt2}^{\,x} = {\sqrt3}^{\,x}$

I am studying logarithms and exponents. I am not sure how to go about solving this problem. I seem too keep going in circles using the rules of log and exp. $$(\sqrt{2})^x = (\sqrt{3})^x$$