why is log(square root) of 100 =1?

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

----

Using your logic then we should call it “P” and not“Pi”. Just as  “Pi” is the sixteenth letter of the Greek alphabet and can have a value other than the ratio of a circle’s circumference to its diameter; so too, can the fifth letter of the Greek alphabet “epsilon” have such a value. The name parenthetically identifies the Greek letter not its value. The “e” comes from Euler and it is clearly identified.

It is more common to identify a mathematical constant by its Greek letter name than to identify the natural logarithm as a Napierian logarithm. (That usage became antiquated over a 140 years ago-- when you were a teenager, learning these things).

My comments are not really a “sneer”. it is more of a “disparaging taunt”. This is not the first error Goldenleaf has made. His error percentages are high.

http://web2.0calc.com/questions/15-2-pi-x-3#r104249 (Divide by 3 to get rid of the exponent)

This isn’t a student making an error. He is teaching/tutoring, and students are potentially exposed to erroneous information. Information which has to be “unlearned.” The competent tutors here are spending a large amount of time correcting his errors.

 Perhaps a little more practice is in order before giving a recital.

My comments toward you are not a sneer either, it’s more “denigrating marginalization.” I’ve seen your work on here. You are a competent, engineering-classed, mathematician why would you tolerate c**p, even if it is wrapped in gold leaf.

Cphill seems to have taken Goldenleaf under his wing. Hopefully that will get rid of the cobwebs and oil up the gears. Maybe, in a few weeks he should be able to play “chopsticks” instead of “chop sewage”.

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.

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 !!

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

----

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

------

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.

 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.  

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

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

http://www.mathsisfun.com/algebra/logarithms.html

Alan is also right - there is no need to aim 'sneers'  OR  'disparaging taunts' at other answerers.  It is not necessary and it is not helpful!

@Anon: As I said before, this si my least favorite thing about math, and that my understanding is rudimentary at best. I knew there were flaws, but I also knew the general answer. That is why I asked for clarification.