# Tagged Questions

Questions related to real and complex logarithms.

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### Solving a logarithmic equation where the logarhitm is exponentiated

I have troubles solving the following logarthitmic equation. $$\ 2(\log_x{\sqrt7})^2-\log_x{\sqrt7}-1 =0$$ The results are supposed to be $\ x_1 = {\frac{1}{7}}, x_2 = \sqrt7$ I have tried ...
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### If $\log_510=\log_7x(\log_nm)$ then the values of x,m and n are?

I have the question that if $\log_510=\log_7x(\log_nm)$ then values of $x$,$m$ and $n$ are? This question looks easy but i tried to get the expression down to the form $$\log_ab=\log_ac\tag{1.}$$ and ...
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### Logarithm common factor problem

there exist positive A, B, and C, with no common factor greater than 1, such that $A.log_{200}5 +B.log_{200}2=C$ what is A + B +C I dont know how to equal this equation
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### Solving a logarithmic polynomial

I want to solve this equation for $x$: $${\frac{1}{\sqrt{2 \pi x}} \left(\frac{e z}{2x}\right)^x} = \epsilon$$ Is there a closed form for it, or does it have to be solved numerically? I can turn it ...
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### The $n$th integral of $\ln(x)$ and fractional derivatives

For a related question, I need to know the $n$th integral of $\ln(x)$ and the fractional derivative of $\ln(x)$. A break down of how fractional derivatives may be found on the Wikipedia. In ...
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### What is the difference between a Logarithm and Scientific Notation? [closed]

Why would you use Logarithms over Scientific Notation and vice versa, since they generally serve some of the same functions?
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### Can someone help me with this question of finding x as exponent?

The equation is: $$6^{x+1} - 6^x = 3^{x+4} - 3^x$$ I need to find x. I forgot how to use logarithm laws. Help would be appreciated. Thanks.
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### $\log(x)$ as iteration-series: how can this be made correct?

I was tinkering with the question whether the logarithm $\log(x)$ can be expressed by some more useful series than by the Mercator series (in terms of (1+x)) for a certain question. One idea ...
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### Solving $y^y = x$ for large $x$

I was playing around with recurrence relations and noticed that $\sqrt x$ has the fun property that $$\frac{x}{f(x)} = f(x)$$ ($\sqrt{x}$ and its negation are the only functions $f(x)$ that satisfy ...
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### Balanced partition of $\{\ln 3, \ln 4,\dots,\ln n\}$

For a positive integer $n\ge 3$, let $A_n=\{\ln 3, \ln 4,\dots,\ln n\}$. Does there exist $N$ such that for all $n>N$, the set $A_n$ can be partitioned into two sets so that their sums differ by no ...
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### Convergence of a sequence of roots of continous functions

Let $(f^n,n\in\mathbb{N})$ be a sequence of complex continous functions so that $f^n(u)\longrightarrow f(u)$ uniformly to a complex continous function f if $n \longrightarrow \infty$. I addition I ...