Questions related to real and complex logarithms.

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1answer
178 views

Solving an exponential equation

Alright, here's the equation: $$‎1.08^x = 1.10^{x-1}$$ I know I need to use logarithms, but I can't figure how to do it. Thanks in advance!
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2answers
273 views

Length of a number

Is there a method which would allow me to precisely calculate length of the largest number which has been created during multiplying two numbers? What I mean is this: 1258 * 2569 Multiplying the ...
1
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1answer
469 views

Why can't you integrate all power functions without a log function?

You need a logarithm function to solve all power functions. That's a fact. Power functions look like this: $f\colon x \mapsto a x^r \qquad a,r \in \mathbb{R}$ But why would you need a logarithm ...
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1answer
157 views

Show the correctness of a logarithmic inequality

Let $p_1>p_2$ and $n_1>n_2$ be positive numbers. I want to show that, $$ \frac{\log \left(\frac{p_1}{n_1}+1\right)}{\log \left(\frac{p_2}{n_2}+1\right)}\leq \frac{\log ...
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2answers
134 views

Stuck on a homework question: if $t = \frac{1}{x}$

If $\displaystyle t = \frac{1}{x}$ then a) Explain why $\displaystyle\lim_{x \to 0^-}f(x)$ is equivalent to $\displaystyle\lim_{t \to -\infty}f\left(\frac{1}{t}\right)$ b) Using that, ...
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2answers
95 views

Solution of equations involving logarithm and simple equation

I have two equations as below: m = c - n m = log(n) + 1 What approach should I take to solve this. I am sorry, I forgot to mention the variables here. 'c' is ...
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1answer
401 views

Is there a binary spigot algorithm for log(23) or log(89)?

The Bailey-Borwein-Plouffe formula yields a binary spigot algorithm for π, and related formulas give the bits of log(2) and those of the logarithms of some other integers. I got stuck (over a year ...
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1answer
290 views

Is the logarithm function injective (one-to-one)?

Is the logarithm function injective (or, one-to-one)? In other words, does $\log_2(x) = \log_2(y) \implies x = y$? I.e., as $x$ and $y$ are in the same log base, can I just drop the logs? Thanks! ...
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2answers
56 views

Plot Line that gets exponentially larger around a point

I'm building a program that calculates the cost of an item based on it's size (let's say a bamboo pole). As the customer requests a longer pole, it gets hard to find a bamboo, plus requires more ...
0
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1answer
238 views

Solving an equation when the unknown is both a term and exponent

I'm taking a course (algorithms) and the instructor assigns us problems from the CLRS Introduction to Algorithms 3rd edition. We aren't marked on the problems, they are just given as exercises. ...
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2answers
1k views

Series of logarithms $\sum\limits_{k=1}^\infty \ln(k)$ (Ramanujan summation?)

I had this question earlier, so to say as a "standalone" problem, but now it pops up in context of an analysis with the lngamma-function. As well as we can convert the question of sums of like powers ...
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2answers
190 views

Homework with logarithms

I'm stuck on continuing the next exercise: Considering: $\log_{c}a = 3$ $\log_{c}b = 4$ and: $$ y = \frac{a^{3}\sqrt{b \cdot c^{2}}}{2} $$ What's the value of $\log_{c}y$ ...
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1answer
184 views

What are logarithms, and what do they do? [duplicate]

Possible Duplicate: Intuitive use of logarithms My math teacher "taught" us about logarithms today, but he didn't give any useful information. He just that one is supposed to "add" them to ...
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2answers
4k views

What is log ? What does it mean? How does it transform a number?

What is log ? What does it mean? How does it transform a number? /I'm a code and see log being used in legacy code I have to change. Thanks
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1answer
2k views

Where did the word “logarithm” come from?

Where did the word logarithm come from? Any relation to the word algorithm?
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2answers
244 views

Notation question: $x\ln^2(1000/y)$ into MATLAB

I've been tasked with working out how much some incorrectly entered calibration coefficients have affected some measurements we've taken. I have the algorithm used, which I can use to work backwards ...
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1answer
1k views

what is “log-average”?

It was mentioned in pLSA paper that perplexity refers to the log-averaged inverse probability on unseen data. Can any one give me the exact formula for calculating perplexity
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1answer
161 views

how to find the value of $\log_3 7$

Can I ask how to compute $\log_3 7$, using the changing the base of logarithm.
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3answers
246 views

how to simplify $\frac{\log_2 625}{\log_2 125}$

How can i simplify this: $\dfrac{\log_2 625}{\log_2 125}$ Thanks
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2answers
113 views

How to solve $(3\log_y 5)(2\log_y 5) / (6\log_y 5)$?

Can I ask how to solve this? $$(3\log_y 5)(2\log_y 5) / (6\log_y 5)$$ the answer is $\log_y 5$.
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2answers
136 views

logarithmic quadratics?

Functions in the form of y = f(x) describe various sorts of line. A line where for every +1 in x then y increases by x is quadratic. A line where for every +1 in x then y doubles is exponential, y = ...
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10answers
2k views

Intuitive use of logarithms

I am trying to gain a more intuitive feeling for the use of logarithms. So my question: what do you use them for? Why were they invented? What are typical situations where one should think: "hey, ...
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0answers
87 views

log bound with floor

In one of my analyses, I am trying to establish a lower bound on $j$. I have the following set of equations: $$u_0 = k$$ $$u_j \geq \lfloor u_{j-1}/2 \rfloor$$ Could I say, $j$ should be at least ...
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1answer
2k views

Normalizing to log

I have an array of numbers I'd like to normalize. Problem is that I do not want a linear normalization. The numbers represent a ranking of people and I want the values to be spread between 0 and 10 ...
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2answers
120 views

Arithmetic error when calculating inverse of the logistic?

I would like to rearrange the logistic function: $$y=\frac1{1+\exp(-a+bx)}$$ To calculate $x=f(y)$ So I did the following: $$\frac1{y}=1+\exp(-a+bx)$$ $$\ln\left(\frac1{y}-1\right)=-a+bx$$ ...
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2answers
74 views

What will the value of following log expression

What will be the value of the expression $$\log_x \frac{x}{y} + \log_y \frac{y}{x}?$$ I tried: $$\log_x x - \log_x y + \log_y y - \log_y x = 1 - \log_x y + 1 - \log_y x = 2 - \log_x y - \log_y ...
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0answers
791 views

Choosing the branch of a logarithm

The problem: I am integrating complex logarithms over an angle $\phi$ over $[0,2\pi]$. It is quite complex (pun not intended) and I called Mathematica in to aid me. I am calculating an energy of a ...
5
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1answer
239 views

Can I build a program that will tell me if a real world data set looks linear, logarithmic, exponential etc?

I have a bunch of real world data sets and from manually plotting some of the data in graphs, I've discovered some data sets look pretty much logarithmic and some look linear, or exponential (and some ...
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4answers
123 views

Solving equality to find upper limit

I need to find a sensible upper limit for a part of an algorithm in a program I am writing. I have boiled it down to this. Given $a$, $b$ and $c$, find $x$ in $a^{x-1}b < c < a^{x}b$. But I ...
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5answers
492 views

$n=8\log_2(n)$, forgot basic math

I'm quite ashamed that I'm at a math-related course at the university and I'm stuck. I can't solve at all this equation: $$n=8\log_2(n).$$ I have tried applying the log property so it becomes $2^n = ...
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4answers
438 views

Please help me to show, that $(\ln x)'=\frac1 x$

In school, we recently started with derivations. I looked into a list of simple derivations and tried to prove them, in order to practice. Now, I tried to find the derivative of $\ln x$, but I got ...
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4answers
12k views

How do I find the base when Log is given

I'm trying to figure out how to calculate the base if: $$ \log_b 30 = 0.30290 $$ How do I find $b$ ? I've slaved over the Wikipedia page for logarithms, but I just don't get the mathematical ...
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2answers
557 views

$\ln(x^2)$ vs $2\ln x$

These two are supposed to be equivalent because of the properties of logarithms, but the domains of $\ln(x^2)$ and $2\ln x$ seem different to me. For example, if I substitute $x=-1$ into the first, I ...
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2answers
417 views

Logarithm of a Markov Matrix

Start with a Markov matrix $\mathbf{M}$, whose elements are all between $0 \le \mathbf{M}_{ij} \le 1$ and each row sums to one. There is a natural connection with this matrix and the rate matrix ...
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2answers
26k views

How to type logarithms in Wolfram|Alpha?

Its sometimes hard to type it if logarithm is not natural and base is not 10, especially if base is variable. So anyone know rules how to type?
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11answers
995 views

Alternative notation for exponents, logs and roots?

If we have $$ x^y = z $$ then we know that $$ \sqrt[y]{z} = x $$ and $$ \log_x{z} = y .$$ As a visually-oriented person I have often been dismayed that the symbols for these three operators ...
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1answer
100 views

Algorithm Math problem help (logarithm ) [closed]

Can you guys show me how you would solve this: logn n^3 = log2 4 =
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1answer
574 views

Convert a sum contain a log function to geometric series

I'm trying to calculate the complexity of an algorithm. I've managed to boil down the cost of the algorithm to the following sum. $$\sum_{k = 1}^{\log_{2}(n)} ...
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2answers
332 views

Logarithm of matrix map?

I am trying to calculate the following $K^{-1}DK^{-1} * p$ Where $K$ is symmetric positive definite and $D$ is positive diagonal and $p$ is a vector. The problem is that p is very, very small so ...
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2answers
165 views

Stuck on a log equation

I am having trouble figuring out how I can solve this log: $$6 \log(x^2+1)-x=0$$ The steps i've thought to take so far are as follows: step 1: subtract the right most x to the other side of the ...
16
votes
2answers
257 views

$2^x - a$ touches $\log_2(x)$

I was playing around with the functions $2^x$ and $\log_2(x)$. As they are the inversions of each other, I thought there was a simple number $a$ for which $2^x - a$ touches $\log_2(x)$. Using ...
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votes
3answers
2k views

How does e, or the exponential function, relate to rotation?

$e^{i \pi} = -1$. I get why this works from a sum-of-series perspective and from an integration perspective, as in I can evaluate the integrals and find this result. However, I don't understand it ...
17
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3answers
575 views

Do you know of any Calculus text defining the exponential and logarithm functions in an alternative way?

The story in nearly every introductory Calculus book is well known by everybody: you don't have the "right" to raise a number to an irrational power, so forget exponents for now and let's take a look ...
3
votes
2answers
270 views

Induction problem: log of product equals sum of logs

Please help me prove by induction that $\displaystyle\forall n\in {{\mathbb{N}}^{*}}$, $\displaystyle\forall {{a}_{1}},\ldots ,{{a}_{n}}\in {\mathbb{R}}^{*}_{+}$, $\displaystyle \ln \left( ...
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2answers
655 views

Find intersection of linear and logarithmic lines

I have equations for two lines, one of which is linear and the other is logarithmic, ie: $$y = m_1 x + c_1$$ $$y = m_2 \cdot \ln(x) + c_2$$ ..and I need to find out where (if at all) these lines ...
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2answers
344 views

Is it standard to say $-i \log(-1)$ is $\pi$?

I typed $\pi$ into Wolfram Alpha and in the short list of definitions there appeared $$ \pi = -i \log(-1)$$ which really bothered me. Multiplying on both sides by $2i$: $$ 2\pi i = 2 \log(-1) = ...
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2answers
210 views

Problems with the number $0$

Here is the original formula: $$\frac{256}{2^x}=y$$ In order to solve for $x$, I've done this: $$\log_{2}\left(\frac{256}{y}\right)=x$$ The problem is that $y$ can be zero. What should I do to solve ...
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votes
4answers
298 views

Does $\log _b \left( x \right) = \log _b \left( y \right) \rightarrow x = y$?

I hit a snag whilst revising some log rules, could anyone confirm my suspicion: $$\log _b \left( x \right) = \log _b \left( y \right) \rightarrow x = y ?$$
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3answers
105 views

How do I solve for $V$ in this equation?

$$\frac{\ln(T+1)-\ln(V-S+1)}{\ln(V-S+1)}=\frac{1}{K}-1$$ What are the steps if I want to solve for $V$?
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1answer
109 views

Number of digits in different number systems?

I know a similar question was asked before, but I wanted to know if this can be extended to any number system by a generic formula. For example, given a number X in number system A, how many digits ...