Tagged Questions

Questions related to real and complex logarithms.

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Solution to initial condition problem

$y=-ln(1-e^{(t+c)})$ I'm trying to find the solution to the initial condition $y(0)=-ln2$ Isolate c $0=ln(2)-ln(1-e^c)$ $0=ln({2\over1-e^c})$ $-e^c=2-1$ $e^c=-1$ $c=0$ I can't figure out ...
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Weighted logarithmic ranking

I want to have a ranking of players by percentage of shots made, weighted by the total number of shots attempted. The weighting should follow a log scale, so for example Player A has 100% accuracy, ...
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What is the argument of the logarithm operator called?

In the expression $ln(y)$, what is '$y$' called. I'm asking for a noun analogous to exponent in $x^n$, where '$n$' is called the exponent. If I'm not mistaken, '$x$' in this case is the radix, or ...
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Is it possible to clear the x using the Lambert function?

$y = \frac{x^2}{4} - \frac{ln(x)}{2}$ Solving, I get to: $e^{4y} = \frac{e^{x^2}}{x^2}$ But I don't know how to continue.
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Stuck solving $\ln(e^y-1)-y=t+c$ for $y$

I'm trying to solve for $y$ $\ln(e^y-1)-y=t+c$ $e^y-1=e^{(t+c+y)}$ $e^y=e^{(t+c+y)}+1$ $y=t+c+y+1$ Where am I going wrong?
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Tricky Logarithmic inequality

I have tried proving this logarithmic inequality but I did not succeed. I tried to put every term on one side, I expanded and tried to use one of the properties of logarithms but the proof does not ...
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Question about the connection between exponential and logarithmic functions

Does this make sense to anyone? What advice would you give me to clarify my reasoning and explanation? One of the really "neat" features of the exponential function: $$f(x)=e^x$$ is the fact that ...
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Lambert W function with natural log

I need to solve the next equation x: $d-x+yln[\frac{d}{x}]=b$ I inserted this into Wolfram Alpha and it returned: $x = y \Bbb{W}[\frac{e^\frac{d-b}{y}d}{y})]$ y, d, b, and x are all real, ...
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Sieve of Eratosthenes Time Complexity Clarification

I've found plenty of sources claiming that the time complexity of the prime sieving algorithm Sieve of Eratosthenes is $O(n\log(\log n))$ where $n$ is the input. However, is this $\log_{10}$ or $\ln$? ...
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Is it possible to simplify $y=100x\cdot\log_{x+1} 2$ (Solved)

Is there any way to simplify the following equation, or any way to reconfigure it in a way that is possible to graph? $$y=100x\cdot \log_{x+1} 2$$
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Computing first k digits and last k digits of a large number using logarithm

How do we compute the first $k$ digits and last $k$ digits of a large number say $2^{N-1}$ for bigger values of $N$ using logarithms? An example for the algorithm will be greatly appreciated. I got ...
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Solve $\sqrt x = 1 + \ln(3 + x)$ algebraically

I am having trouble with this homework problem. I am able to graph and find the solution, but I am curious as to how one would do this algebraically. The way I began, was subtracting $1$ on both ...
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Evaluating right hand limit for a function

I want to prove the following right-hand limit (one sided limit) using $\epsilon-\delta$ definition; $\lim_{u\to 0^+} {u^{s_0} f(-ln u)} = 0$ where $f$ is a function from $R \to R$ and $s_0$ is a ...
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A limit concerning the integral of $x^n$

I pondered if the general integral of $x^n$ could be used with limits to prove that $$\int x^{-1}dx=\ln(x)+C$$ I started with $$\int x^ndx=\frac1{n+1}x^{n+1}+C$$ Then, I took the limit as $n$ ...
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How do i solve these exponential equations? [closed]

Is there a way to solve these exponential equations without using logarithms? I tried to get the same base for all the terms, but I could not make it. Is there any other general procedure that I can ...
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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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Express $y$ in terms of $x$ in logarithmic graph

Express $y$ in terms of $x$: I know that $y = mx + c$ translates to: $\log y = n \log x + \log c$ All I can see in the question 2a of the graph below. I can tell that from the graph in question ...
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Show that $y=e^{e^{cx}}$ is a solution of the differential equation $\frac{d^2y}{dx^2} =c^2 \cdot y \cdot \ln(y) (1+\ln(y))$

Question: Show that $y=e^{e^{cx}}$ is a solution of the differential equation $$\frac{d^2y}{dx^2} =c^2 \cdot y \cdot \ln(y) (1+\ln(y))$$ I know there are a lot of ways of solving this and I ...
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Prove $\log(n!) =\Omega(n\log(n))$ [closed]

Can someone help me prove that $\log(n!) =\Omega(n\log(n))$, that is, that there exists some positive $c$ such that, for every $n$ large enough, $\log (n!)\geqslant c\cdot n\cdot \log(n)$?
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Can anyone help me figure out how to go from the first expression to the second? $$$$\ln D=u+\delta(e-p)+\gamma y-\sigma r$$$$ $$\pi \ \ln (D/Y)= \pi[... 2answers 31 views For what values are these logarithms true? For what values, x and y, are both these equations true?$$\frac {\log(x)}{\log(y)} = \frac 23$$AND$$\frac xy = \frac 23$$How would one solve this? 0answers 63 views Natural Logarithm Integration For what set of functions is \int \frac{\ln{f(x)}}{f'(x)}\mathrm{d}x defined? More specifically related to the reason I ask, when$$ f(x) = \frac{c}{x} + \arcsin{x} + \sqrt{\frac{1}{x^2}-1}  is ...
I have a problem solving the below equation with respect to $x$: $0.6\cdot \exp(\frac{-40}{x})+0.4 \cdot \exp(\frac{10}{x})=1$ My problem is that I have two exponential functions which are added ...