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Your question makes no sense.

I just want to 'play' with this question for a moment.

I am going to cosider the equation

0=3x^2+12x+5

$${\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{5}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{21}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}\right)}{{\mathtt{3}}}}\\
{\mathtt{x}} = {\frac{\left({\sqrt{{\mathtt{21}}}}{\mathtt{\,-\,}}{\mathtt{6}}\right)}{{\mathtt{3}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{3.527\: \!525\: \!231\: \!651\: \!946\: \!7}}\\
{\mathtt{x}} = -{\mathtt{0.472\: \!474\: \!768\: \!348\: \!053\: \!3}}\\
\end{array} \right\}$$

So I could say

$$3x^2+12x+5 = \left(x+\frac{\sqrt{21}+6}{3}\right)$$ $$\left(x-\frac{\sqrt{21}-6}{3}\right)$$ and I could factor out 9.

I would do that but LaTex is playing up and I cannot be bothers with it anymore!

Anyway, I can do that can't I?

You are on notice.

Restrain yourself or your answers will be removed from the forum and all your efforts will be for nought!

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My Lady Guinevere, I made no disparaging slight against the court jester in this post. Your lowly servant only disagreed with the supposition that the barber be a child.

Please, I pray thee spare mine head. Morgan le Fay hath vexed me, and placed a cursed upon me, compelling an allergy of severity that manifests itself when dense fog or something close it is near to thine kingdom.

Could you spare a kerchief?

Your lowly servant,

Morgan Tud

I would like this to be shown on a diagram.  The logic behind the formula is beneficial.

It would have been a really good answer if it didn't contain the slight against GoldenLeaf.

You are on notice.  

Restrain yourself or your answers will be removed from the forum and all your efforts will be for nought!

$$y=log_{10}(\sqrt{100})\\\\
y=log_{10}10$$

Now, A LOGARITHM IS A POWER  (or exponent)

$$10=10^y$$

$$y$$ is obviously 1

Therefore   $$log_{10}(\sqrt{100})=1$$

There are other ways to show you the same thing, which is why there are so many answers.

Have a look here

He/she is almost right (though it's sad he/she felt the need to sneer), but the word "epsilon" isn't really appropriate. … . by Alan

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happiness,aims,dreams that is what life is that is what everyone wishes to achieve the beauty of it is how to achieve it and will you achieve it, so basically its like a vedio game your trying to finish by for example getting the crown 

hope that helped

2

0.000002204 = 2204/1000,000,000 = 551/250,000,000

There are 9 numbers after the 0

so the denominatore will be 1 followed by 9 zeros.

$$\frac{2204}{1000000000}$$

This can then be simplified.

 Anonymous wrote: A natural logarithm is NOT in base 10. The base is e (epsilon). 

He/she is almost right (though it's sad he/she felt the need to sneer), but the word "epsilon" isn't really appropriate.  The e in question is just the number e = 2.718281828459...etc.  The natural logarithm is also sometimes called the Napierian logarithm after John Napier (1550-1617) who invented logarithms.

Logarithms to base 10 are sometimes referred to as common logarithms.  

More sounds of BS happening ….

The barber is a young child with a steady hand … by GoldenLeaf

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A young child is not a man, GoldenLeaf.

(Oh, the barber could be a woman. Again, the barber is defined as a man. But if she is trans-gender, she might need a barber. This can go on for a long time).

This paradox, though Zen-like, is a actually a construct to explain Russell's Paradox. The structure of the argument is set to create a circular paradox.

Consider Russell's Paradox:

Define Naive Set Theory (NST) as the theory of predicate logic with a binary predicate and the following axiom schema of unrestricted comprehension (an impossible task, for most humans):

for any formula P with only the variable x free. Substitute for . Then by existential instantiation (reusing the symbol y) and universal instantiation we have

a contradiction. Therefore NST is inconsistent.

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This is not a solution for the Zen-like question, but it begins to show why there may not be a (non-quantum) solution.

There is a legend this circular argument came from Sir Cumference of the Round Table, after hearing of a brave knight who wished to serve his king:

So there was this knight, Sir Lancelot, and he was summoned by King Arthur to deliver an important message to the neighboring kingdom and told him to saddle up a horse and ride.

Sir Lancelot says, “But your highness, it' s thundering and raining and lightning outside.

”But,” the king says, “it’s important and you must go.“

Sir Lancelot goes to the stables, but finds no horses, just a large Great Dane. He reports back to King Arthur with the Great Dane in tow and says, “Sire, there are no horses, but if you want me to, I will saddle up this Great Dane and ride out into the storm.”

“Never mind,” says King Arthur, “I wouldn’t send a knight out on a dog like this.”

A circular pun leads to a circular paradox.

What is the sound of BS happening? See below for an answer.

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A natural logarithm is just in base10. …

... This works because the square root of 100 is 10, and since 10 is a dual factor of, well, 10, the natural logarithm can be taken of it and the answer is one.

...

by GoldenLeaf

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A natural logarithm is NOT in base 10. The base is e (epsilon). Sometimes called Euler's number. The natural log of 10 is 2.30258509… .

You should change your name to “Pyriteleaf”.

There was once a mathematician who won a gold medal. He like it so much he had it bronzed.

Good answer, GoldenLeaf !!!

Now...as to your question......in Zen practice, the answerer is not expected to always give an answer. In fact, there may BE no answer. Contemplation about the answer is sometimes more important that the "correct" answer itself.

I'm still contemplating...........

Your answer was fine, GoldenLeaf.  Let me see if I can add to it.

Note, that by a property of exponents,we can write √(100) as 100^1/2 

So we have.......log√(100) = log(100)^1/2

And by a property of logs we can write log (a)^b  = b log (a)

So we an write log(100)^1/2  as (1/2) log (100) ......which we also can write as (1/2) log₁₀ (100)

Don't get too frustrated by a log...it's just an exponent (power)...basically, we're asking ourselves what power (exponent) do we need to put on the "little" 10 to raise it to 100??  Answer........2.

So log₁₀ (100)  = 2

And...... (1/2) [log₁₀ 100]  =  (1/2) [2]  = 1

And there you go !!

Hope that helps !!

@CPhill The barber is a young child with a steady hand, and thus has not reached the age where he is ready to shave himself.

So we have

(y/15) = (7/3)

Using cross-product equality, we have

3y = 15*7

3y = 105 

divide by 3

y = 35

Here's another method that sometimes works well. What did I have to multiply 3 by in the denominator of the second fraction to get 15 in the denominator of the other??  Answer, 5.  So, if I multiply the 7 in the numerator of the second fraction by 5, I get 35 for "y" in the numerator of the first fraction.

Remember, logarithms are really, really complicated. This is literally my least favorite thing in math. As such, this wil probably be a very basic and completely unhelpful while still having a somewhat correct answer.

A natural logarithm is just in base10. Since it is in base10, all numbers that are 10^whatever are whole numbers when the logarithm is taken of it. As such, numbers such as 10, 100, 1000, and really long numbers like 1000000000000000000000000000000000000000000 are all able to have the natural logarithm taken of them.

Thus, the below equation is what I'm guessing you were trying to portray, correct?

$${log}_{10}\left({\sqrt{{\mathtt{100}}}}\right) = {\mathtt{1}}$$

This works because the square root of 100 is 10, and since 10 is a dual factor of, well, 10, the natural logarithm can be taken of it and the answer is one.

It would help if somebody who understood this better could give a more in-depth and sensible answer.

A simple ratio/proportion problem.

y:15 = 7:3

y/15 = 7/3

y/15 = 35/15

y = 35

Sunday 11/5/14   #####

A couple of interesting questions/answers

So, we have the points (2,5) and (6,-1).

I have a "nonstandard" method for finding slope.

Put the points one over another - it doesn't matter which point goes over the other - like this:

(2 , 5)

(6 , -1)

Now, just "subtract" the second from the first. This gives:

(-4 , 6)

Now, put the first thing "under" the second.........6 /-4  = -3 / 2 and there's the slope !!!

To find the slope of the graph of f, you would have to make two coordinates from each of them which would be (2,5) and (6,-1), then use the formula y₂- y₁ over x₂ - x₁ to get the slope of f for your answer.  

I would help you with this question, if I knew exactly what the question is.....