# Tagged Questions

Questions related to real and complex logarithms.

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### An alternative way to calculate $\log(x)$

How can I replace the $\log(x)$ function by simple math operators like $+,-,\div$, and $\times$? I am writing a computer code and I must use $\log(x)$ in it. However, the technology I am using does ...
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### Find the product of $\log_{2005}(1/2)\log_{2004}(1/3)\log_{2003}(1/4)\cdots\log_2(1/2005)$. The bases are $2005,2004,2003,\ldots,2$ [closed]

This question was answered in this site itself by Mark Bennet. But I didn't understand how the logs got cancelled out.
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Imagine I have three sets of strictly positive real numbers: $a_i,b_i,c_i>0$, $\forall i=1,\ldots,n$. For finite $n$. And further that the following inequality holds: \begin{align} \sum_i a_i \leq \...
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### Question on logarithm Exponentiation

I know it's not the best title but I had no idea how to be specific about it. Basically what I'm looking for is a rule that states how $$\log^2(a^{f(x)})$$ works. Does it become $$f(x)\log^2(a)$$ or ...
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### Show that xy=100. Given $2\log x^3y=6+3\log y-\log x$.

Given $2\log x^3y=6+3\log y-\log x$, x and y are positive integers. Show that $xy=100$. I have tried until $x^7=10^6 y$. Now, my problem is how to prove $x=y$.
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### Laurent series of logarithm

Lets have a function $$f(z)=\ln(\frac{z-a}{z-b})$$ on the region where it is holomorphic(off course). I want to find the laurent series for this function. Now finding the taylor expansion of this ...
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### Calculating the mass xkg of radio-active substance pertaining to days after starting timing

Just testing myself with some tricky questions in my further maths textbook. This one states that the mass xkg of a radio-active substance remaining in a sample t days after starting timing is given ...
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### What is the difference in this question between $\log$ and $\lg$?

Am I right in assuming that $\lg$ just refers to $\log$ base ($10$)? Whereas $\log$ is just any unspecified log? I'm solving $\lg{15}-\lg{5}$ Am I good to just use the standard rules of logarithms, ...
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### Integrate a power of logarithm [closed]

Is there some way, how to solve this problem? $$\int \ln^n(x) dx \text{, where } n \in \mathbb{N}$$ I really don't know, what to do with $n$.
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### Suppose there is $log_{a}^{*}x$ and $\log_{b}^{*}x$ then $\log_{a}^{*}x = O(\log_{b}^{*}x)$

Consider two $a,b \in R$. So my question is : Suppose there is exist $log_{a}^{*}x$ and $\log_{b}^{*}x$ then $\log_{a}^{*}x = O(\log_{b}^{*}x)$ NB: $\log^{*}{n} = 1+\log^{*}{\log{n}}$ Actually I ...
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### Show that $\sum _{k=1} ^N \frac 1 {\sqrt {k^2 + 1} + k} > \frac 1 2 \ln \frac {2N+1} 3$, where $N$ is natural number.

Show that for $N = 1,2,3,\dots$ we have $$\sum _{k=1} ^N \frac 1 {\sqrt {k^2 + 1} + k} > \frac 1 2 \ln \frac {2N+1} 3$$ I got this as a calculus homework. I am supposed to show this, but it doesn'...
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### can someone explain this simplification for me?? [closed]

Can someone tell me how $$−56−173\,\ln(11)+366\,\ln(13)−\left(\frac{105}2+20\,\ln(2)+366\,\ln(3)\right)$$ simplifies to $$\frac{-217}2−20\,\ln(2)−173\,\ln(11)+732\,{\rm arctanh}\left(\frac58\right)?$$ ...
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### Logarithmic square

I can't understand if there is any such formula for $(\log_{b}a)^2$. Are there any? $\log_{b}(a^2) = 2\log_{b}{a}$ But if the whole log is squared is there any such formula or the same formula is ...
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### Ascertaining a from logarithmic equations

I've just been accepted on to a PHD program at Melbourne, studying chemical engineering. I'm working my way through some standard pure and further mathematics books just to get the concepts into my ...
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### Finding the solution of logs and exponentials equations to 2 decimal places

I'm going through maths textbooks at a rather fast pace at the moment as I have been accepted to take my chemical engineering PHD in Melbourne next year. I have been doing really well at the log ...
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### How to solve $3^{\sqrt{\log_{3}{x}}}+x^{\sqrt{\log_{3}{x}}}=6$

How can i solve the following equation? $$3^{\sqrt{\log_{3}{x}}}+x^{\sqrt{\log_{3}{x}}}=6$$ It is clear that $x=3$ is a solution of this equation. But how can i prove that there is another solution ...
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### Solve for x: $4\log_{x/2}(\sqrt{x}) + 2 \log_{4x} (x^2) = 3 \log_{2x} (x^3)$

$$4\log_{x/2}(\sqrt{x}) + 2 \log_{4x} (x^2) = 3 \log_{2x} (x^3)$$ This is a different type of equation. Our school has not taught this type yet. But this came in our exams. Can someone please help? ...
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### Pollard Rho - DLP Algorithm Implementation

I am working with Pollard Rho Algorithm DLP. I have developed in Java and Python the way to calculate the table to find the collisions, and then using congruences and some others tricks I am getting ...
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### Logarithm problem question

$$a^{bx} = c$$ Solve for x $$\log a^{bx} = \log c$$ $$bx \log a = \log c$$ $$x = \frac{\log c}{b \log a}$$ Is this correct? Thanks :)