Tagged Questions

Questions related to real and complex logarithms.

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Identities derived from Euler's Identity

I am just learning about Euler's identity. When messing around with it, I am getting some unsettling identities, which, I believe, is probably due to my lack of application of certain rules. Starting ...
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Finding intersection between functions containing logarithms

At what point does $8x^2$ and $64x\log(x)$ intersect? I'm trying to catch up on my math, but this stumped me. Something awry in my understanding of logarithms. I figured that I could equate both ...
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If a>0 a is not equal to 1 then the equation

$2 \log_x (a)+ \log_{ax} (a) + 3\log_{a2x} (a)=0$ then he equation has how many real roots?? The above problem is a quadratic equation problem.
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Sum of Logarithms of expoenetial functions

Given a matrix $P \in \Re^{n \times d}$, and a column vector $\theta \in \Re^d$. Assume that $\sum\limits_{i=1}^n \ln{(1+e^{P_i\theta})} \leq 1$, where $P_i$ is the $i^{th}$ row in $P$. What can be ...
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Difference between branches $[-\pi, \pi)$ and $[\pi, 3\pi)$ of the complex logarithm

I think that both branches just exclude the negative part of the real line. So what's the difference between them then?
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norma distribution and log-normal distribution

I often see when people analyzing data, they assume data has either normal or log-normal distribution, and trying to fit data into a distribution for the convenience of data analysis (e.g. by ...
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How do you calculate what $k$ is? [on hold]

How do you calculate what $k$ is? $$\frac{d-1}{k} = \log \left(\frac{21}{100} d\right)$$ And how do I get the integer value?
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how to proceed next in this logarithmic inequality?

The question is $$\frac{1}{\log_4{\left(\frac{x+1}{x+2}\right)}}<\frac{1}{\log_4{(x+3)}}$$ I did the first step for defining the arguments of both sides and got $x\in(-3,-2)\cup (-1,\infty)$ ...
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