In general, one doesn&#39;t expand out `log(a + b)`; you just deal with it as is.  That said, there are occasionally circumstances where it makes sense to use the following identity:

    log(a + b) = log(a * (1 + b/a)) = log a + log(1 + b/a)

(In fact, this identity is often used when implementing `log` in math libraries).

I have read [this thread][1] but I&#39;m wondering how secure such a solution would be? I know that github offers ssh/ssl support and am familiar but could someone give me a breakdown of what sort of internal security they would use to make sure my committed conf/credential files don&#39;t get hacked?

**EDIT**: I&#39;ve read http://help.github.com/security/ but I would like an answer from someone who has worked with multiple repository hosts and has real-world experience with this.


  [1]: https://stackoverflow.com/questions/109440/best-git-repository-hosting-for-commercial-project

How secure would github hosting be for private repositories?

So I&#39;ve got ZSH doing all this cool stuff now, but what would be REALLY awesome is if I could get it to run &#39;ls -a&#39; implicitly after every time I call &#39;cd&#39;. I figure this must go in the .zlogin file or the .aliases file, I&#39;m just not sure what the best solution is. Thoughts? Reference material?

ZSH: automatically run ls after every cd

I would like to know the complete expansion of `log(a + b)`.

For example

    log(a * b) = log(a) + log(b);
    log(a / b) = log(a) - log(b);

Similar to this, is there any expansion for log(a + b)?

How to expand and compute log(a + b)?

I would like to know the complete expansion of <code>log(a + b)</code>.
For example
<pre><code class="hljs language-scss">log(a * b) = log(a) + log(b);
log(a / b) = log(a) - log(b);
</code></pre>
Similar to this, is there any expansion for log(a + b)?

Given the following RSA keys, how does one go about determining what the values of *p* and *q* are?

    Public Key: (10142789312725007, 5)
    Private Key: (10142789312725007, 8114231289041741)


Cracking short RSA keys

I have no idea how to do this? I&#39;m adding comma numbers, result is of course always a number with way too many digits after the comma. anyone?

Rounding numbers to 2 digits after comma

Are there any functions (as part of a math library) which will calculate [mean][1], median, mode and range from a set of numbers. 


  [1]: http://www.cimt.plymouth.ac.uk/projects/mepres/book8/bk8i5/bk8_5i2.htm

How to calculate mean, median, mode and range from a set of numbers

What would be the easiest way to calculate Greatest Common Divisor and Least Common Multiple on a set of numbers? What math functions can be used to find this information?

How to find GCD, LCM on a set of numbers

In **JavaScript**, how do I get:

 1. The whole number of times a given integer goes into another?
 2. The remainder?

How to perform an integer division, and separately get the remainder, in JavaScript?

My knowledge of big-O is limited, and when log terms show up in the equation it throws me off even more.  

Can someone maybe explain to me in simple terms what a `O(log n)` algorithm is? Where does the logarithm come from?

This specifically came up when I was trying to solve this midterm practice question:

&gt; Let X(1..n) and Y(1..n) contain two lists of integers, each sorted in nondecreasing order. Give an O(log n)-time algorithm to find the median (or the nth smallest integer) of all 2n combined elements.  For ex, X = (4, 5, 7, 8, 9) and Y = (3, 5, 8, 9, 10), then 7 is the median of the combined list (3, 4, 5, 5, 7, 8, 8, 9, 9, 10). [Hint: use concepts of binary search]

What would cause an algorithm to have O(log n) complexity?

This is my first course in data structures and every lecture / TA lecture , we talk about `O(log(n))` . This is probably a dumb question but I&#39;d appreciate if someone can explain to me exactly what does it mean !?

Difference between O(n) and O(log(n)) - which is better and what exactly is O(log(n))?

Using numpy, how can I do the following:

    ln(x)

Is it equivalent to:

    np.log(x)

I apologise for such a seemingly trivial question, but my understanding of the difference between `log` and `ln` is that `ln` is logspace e?

How do you do natural logs (e.g. &quot;ln()&quot;) with numpy in Python?

It seems that the `set_xticks` is not working in log scale:

    from matplotlib import pyplot as plt
    fig1, ax1 = plt.subplots()
    ax1.plot([10, 100, 1000], [1,2,3])
    ax1.set_xscale(&#39;log&#39;)
    ax1.set_xticks([20, 200, 500])
    plt.show()

is it possible?

set ticks with logarithmic scale

I was just testing an example from *Numerical Methods in Engineering with Python*.

    from numpy import zeros, array
    from math import sin, log
    from newtonRaphson2 import *
    
    def f(x):
    	f = zeros(len(x))
    	f[0] = sin(x[0]) + x[1]**2 + log(x[2]) - 7.0
    	f[1] = 3.0*x[0] + 2.0**x[1] - x[2]**3 + 1.0
    	f[2] = x[0] + x[1] + x[2] -5.0
    	return f
    	
    x = array([1.0, 1.0, 1.0])
    print newtonRaphson2(f,x)

When I run it, it shows the following error:

    File &quot;example NR2method.py&quot;, line 8, in f
        f[0] = sin(x[0]) + x[1]**2 + log(x[2]) - 7.0
    ValueError: math domain error

I have narrowed it down to the log as when I remove log and add a different function, it works. I assume it is because of some sort of interference with the base, I can&#39;t figure out how. Can anyone suggest a solution?

Content Type	Original Author	Original Content on Stackoverflow
Question	Aditya Singh	View Question on Stackoverflow
Solution 1 - Math	Stephen Canon	View Answer on Stackoverflow

How to expand and compute log(a + b)?

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Solution 1 - Math

ZSH: automatically run ls after every cd

How secure would github hosting be for private repositories?

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