Tagged Questions

Questions related to real and complex logarithms.

168 views

91 views

100 views

The diferential equation $y' = \frac{\ln(x^2+y^2)}{x^2 + y^2}$

In my University, the integral calculus teacher gave me this diferential equation to solve. $$y' = \frac{\ln(x^2+y^2)}{x^2 + y^2}$$ I dont have any clue of what form has the solution of this ...
92 views

61 views

Is the product rule for logarithms an if-and-only-if statement?

If a function $f(x)$ is proportional to $\ln x$, then we know $$f(xy) = f(x) + f(y).$$ My question is, Is the converse true? If we know that, for an unknown function f, $$f(xy) = f(x) + f(y),$$ ...
216 views

Solving an exponential equation without the quadratic formula

High school math student here. In my homework I was asked to solve $16^x +4^{x+1} - 3= 0$ and I used substitution to get $x=\log_4{(-2+\sqrt7)}$. However, this was in the chapter on ...
83 views

Inverse of $x^2+\log^2\cos x$

I'm looking for the inverse of $$f(x)=x^2+(\log\cos x)^2$$ Where $f$ is defined from $[0,\pi/2)$ It dosen't have to be closed form, a sum, an integral or some special functions would be of interest ...
49 views

Exercise concerning logarithms…

I have such a problem: find all the values of real parameter "a", for which the following inequality is true for any "x" that belongs to R. I will show you my solution, and please can you verify ...
112 views

Fourier transform of a logarithm

How can one go about computing the 2d (or 1d, in either variable) Fourier transform of the function $$\ln(w^2-k^2)?$$
93 views

28 views

71 views

Tweaking Reddit's Ranking Algorithm

This image explains how Reddit's Ranking algorithm works. As you know, Reddit is a very high traffic site. Therefore, the post rank decreases quite fast. This algorithm puts emphasis on bringing ...
57 views

Solve $x=C \log(C \log(x+A)+B)$

Is it possible to resolve an equation of the type $$x=C\log{(C\log{(x+A)}+B)}$$ (where $A$, $B$, and $C$ are real-valued parameters) for $x$? As far as I can see, the function on the right hand ...
137 views