3
votes
5answers
202 views

Can this log question be simplified?

$ { 2^{log_3 5}} -  {5^{log_3 2}}.$ I don't know any formula that can apply to it or is there a formula?? Even a hint will be helpful.
0
votes
2answers
37 views

Simultaneous log equations

I'm going through logarithms at the moment, and I can't solve this simultaneous equation: $$\log x - \log 2 = 2\log y$$ $$x - 5y + 2 = 0$$ I've tried substituting both $x$ and $y$ to no avail: ...
1
vote
0answers
20 views

Combining ±% with ±dB in measurement uncertainty

Firstly apologies if this is not the correct place to post this but wasn't sure which site would be good to ask regarding about measurement uncertainty calculation. I am trying to calculate the ...
4
votes
2answers
83 views

Non-integral power of a singular matrix

I know, that if $A$ is nonsingular matrix, so $\det{A} \ne 0$, then $A^p=\exp\left(p\ln A\right)$ is true for any real exponent, but what about if $A$ is singular? Then $A$ has a zero eigenvalue, so ...
1
vote
3answers
78 views

Solution for $x$ with exponents?

I am trying to solve the following, $$7^{(2x+1)} + (2(3)^x) - 56 = 0$$ Should I put the 56 on the other side and get the log of both sides and is there a better way to solve this.
0
votes
0answers
39 views

Scaling a big range of small numbers to a small range of big numbers

I'm trying to make a volume meter in a Flash program. I have data coming in like: 0.008 0.0005 0.1 0.02 These numbers indicate the volume of a sound coming in ...
2
votes
2answers
81 views

Question that can not be solve analytically .

You can know that the solution of this non-linear simultaneous equations is y=2 and x=3; but the question is : How can mathematically ( algebraically ) find this. \begin{array}{lcl} x^y & = & ...
2
votes
2answers
78 views

Does log of a matrix factor through similarity? Is it a bijection up to branch choice?

When taking the log of a matrix we have various choices, but fixing a particular choice, we should have $$P^{-1}\log{(A)} P = \log(P^{-1}AP),$$ right? (Here $P \in GL$.) It is supported by the ...
4
votes
4answers
116 views

Simple looking log problem

How would I solve this for $x$? The original problem is $$x+x^{\log_{2}3}=x^{\log_{2}5}$$ I have tried to reduce it down to this, $$x^{\log_{10}3}+x^{\log_{10}2}=x^{\log_{10}5}$$ I have been ...
1
vote
2answers
62 views

determine x in $x\log_\frac{1}{10}(x^2+x+1)>0$

I wanted to know, how can i determine the values of x for which $x\log_\frac{1}{10}(x^2+x+1)>0$ going to the question, we must have $x>0$ and $\log_\frac{1}{10}(x^2+x+1)>0$ or both must ...
3
votes
2answers
55 views

Logarithm inequality for vectors

I am trying to prove the following result. Let $d$ be a vector in $\mathbf{R}^{n}$ with $\|d\|_{\infty} < 1$. Then, $$ \sum_{i=1}^{n} \log(1 + d_{i}) \geq \mathbf{1}^{T} d - \frac{\|d\|_{2}^{2}}{2 ...
1
vote
1answer
106 views

All the logarithms of a non-singular matrix.

I'm reading some notes on dynamical systems that talk about matrix logarithms with little to no detail on the subject. I read the wikipedia article and others on the internet, but not all is clear. ...
0
votes
2answers
3k views

How to enter subscript characters in WolframAlpha? [closed]

I'm trying to enter equations like this in WolframAlpha. How do I format this?
1
vote
1answer
86 views

Is $e^{\alpha\log(M)}$ equal to $M^{\alpha}$?

Supposing the matrix logarithm exists, is $e^{\alpha\log(M)}$ equal to $M^{\alpha}?$ This equality obviously holds for positive reals, but does it also hold for matrices?
3
votes
1answer
157 views

How to prove $\left\|\ln\left(e^{iH_1}e^{iH_2}\right)\right\|\leq\left\|H_1\right\|+\left\|H_2\right\|$?

Let $H_1$ and $H_2$ denote arbitrary Hermitian operators (finite dimensional) and let $\left\|\ldots\right\|$ denote the usual operator norm. I conjecture that $$ ...
3
votes
3answers
2k views

Value of Logarithm of negative number

Why the logarithmic value of negative number can't be define? Is there any special reason?
1
vote
4answers
66 views

Simplifing logarithmic equation

I have the result of a differential equation to be: $$\ln(x+3)=3\ln(t+2)+C$$ I want this to be as simplified as possible. Can it be proceeded like: $$e^{(x+3)}=3e^{(t+2)+C}$$ I am not sure about ...
0
votes
1answer
35 views

Specific range of numbers is given, trying to get another number within same range

I'm trying to calculate the width of an HTML element based on the window size. Here's what I have. These width values (first value) accurately match with the width the HTML element must be (second ...
0
votes
1answer
260 views

How to learn graph plots of math functions?

I really don't know how to we say that a log function would look like this or polynomial function would look like this. I know that if I have like $X + Y = c$, I can draw straight line by taking ...
1
vote
1answer
150 views

Can you use a logarithm coefficient in a linear equation?

I have an equation that looks like $x+(\ln3)y+z=0$ where there's a natural logarithm as a coefficient. Is it possible to have this in a linear equation? I know that you cannot have a root or a product ...
5
votes
1answer
240 views

Can I build a program that will tell me if a real world data set looks linear, logarithmic, exponential etc?

I have a bunch of real world data sets and from manually plotting some of the data in graphs, I've discovered some data sets look pretty much logarithmic and some look linear, or exponential (and some ...
5
votes
2answers
424 views

Logarithm of a Markov Matrix

Start with a Markov matrix $\mathbf{M}$, whose elements are all between $0 \le \mathbf{M}_{ij} \le 1$ and each row sums to one. There is a natural connection with this matrix and the rate matrix ...