#### Eclectic Mystic

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I'll start:

Who understands what logarithms are?

OK, go!

Who understands what logarithms are?

OK, go!

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- Thread starter Eclectic Mystic
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I'll start:

Who understands what logarithms are?

OK, go!

Who understands what logarithms are?

OK, go!

I'll start:

Who understands what logarithms are?

OK, go!

With not too much thought, the answer should come to you.

What is 23 x 24.

The answer is 2 7 which is obtained by adding the powers 3 and 4. This is correct, of course, since 23 x 24 is just seven 2s multiplied together. Note that this addition trick does not work for the case of 33 x 24. The base numbers must be the same, as in the first case, where we used 2.

In general, this addition trick can be written as pa x pb = pa+b. This expression will do our job of multiplying any two numbers, say 1.3 and 6.9, if we can only express 1.3 as pa and 6.9 as pb.

What number will we use for the base p? Any number will do, but traditionally, only two are in common use:

Ten (10) and the transcendental number e (= 2.71828...), giving logarithms to the base 10 or

If you would like to know why this strange number e is used click here.

1.3 = 10a

`a' is called "the logarithm of 1.3". How large is `a'? Well, it's not 0 since 100 = 1 and it's less than 1 since 101 = 10. Therefore, we see that all numbers between 1 and 10 have logarithms between 0 and 1. If you look at the table below you'll see a summary of this.

1 - 10 or 100 - 101

10 - 100 or 101 - 102

100 -1000 or 102 - 103

etc.

0 -1

1 - 2

2 - 3

etc.

You see, we have the number range listed on the left and the logarithm range listed on the right. For numbers between 1 and 10, that is between 100 and 101, the logarithm lies in the range 0 to 1. For numbers between 10 and 100, that is between 101 and 102, the logarithm lies in the range 1 to 2, and so on. Now in the bad old days before calculators, you would have to learn to use a set of logarithm tables to find the logarithm of our number, 1.3, that we asked for earlier. But nowadays, you can get it at the press of a button on your calculator.

Most calculators are very straightforward in obtaining the logarithm. They either have two logarithm keys or a dual function key. In any case, the labels will be `log' and `ln' which is often pronounced

Log is the key for logs to the base 10 and ln is for natural logs. We want logs to the base 10 in our example so we use `log'. Enter 1.3 on your calculator, and then press the

Do you have 0.113943? You should have. This number then is `a' back in our previous expression and therefore the logarithm of 1.3. Pause now and determine `b' in that expression, the logarithm of 6.9.

You should have 0.838849 for the log of 6.9. If not, review what we have done and try again. Now we are going to do something silly in view of the fact that you have a calculator. We're going to use the two logarithms you have evaluated to find the product of 1.3 and 6.9. Of course, you can do it quickly with your calculator, but this will show that logarithms do what they are supposed to do. According to our original idea, the sum of the two logarithms was supposed to be the logarithm of the answer.

Now add the two logarithms. The sum is 0.952792. This is the logarithm of the answer. If we only knew what number had 0.952792 as its logarithm, we would know the value of 1.3 x 6.9.

The problem of finding a number when you know its logarithm is called finding the

You should look for a key on your calculator that says something like 10x or 10y. If so, then pressing that key will take the antilog of the number in the display. Alternatively, your calculator may have an

Did you get 8.97? If not, try again. Of course, you might have got something like 8.96999 but of course that really is 8.97. Now, multiply 1.3 x 6.9 on your calculator and you'll see that 8.97 is indeed the correct answer.

The whole operation could be done with natural logarithms as well as shown below.

1.3 x 6.9 = ?

ln 1.3 = 0.262364

ln 6.9 = 1.931521

total = 2.193885 i.e. 1.3 = e0.262364

i.e. 6.9 = e1.931521

i.e. 1.3 x 6.9 = e2.193885

antiln 2.193885 = 8.97

In the table below, I've taken the difference between the ln of 1.3 and the ln of 6.9. Check it on your calculator.

1.3/6.9 = ?

ln 1.3 = 0.262364

ln 6.9 = 1.931521

ln 1.3/6.9 = -1.669157

antiln (-1.669157) = 0.1884Don't be afraid of the negative sign. It simply means that the answer is less than 1. Enter -1.669157 on your calculator, then find its antiln. Note we are working with natural logs in this example.

If you didn't get 0.1884, try again. Of course, this is just 1.3 divided by 6.9. In the table below, I have done the whole problem over again using common logs. Pause here and check it. log 1.3 = 0.113943

log 6.9 = 0.838849

log(1.3/6.9) = -0.724906

antilog (-0.724906) = 0.1884

For example, suppose you have a certain number of radioactive atoms at time t = 0. Let's let this number be N0. Radioactivity behaves in such a way that the number N of radioactive atoms remaining at a later time t is given by a linear variation of the logarithm of N with t.

ln N - ln N0 = -kt.

But we know that the difference of logarithms is the logarithm of the quotient so the left-hand side becomes ln N/N0. Now let's take antilogarithms and do the right side first. The antiln of any quantity is the number e to the power of that quantity so the right-hand side becomes e-kt. The left-hand side is the antiln of the ln and so it just becomes N divided by N0. Finally, we can rearrange to put the final equation in the form

N = N0 e-kt

which is called the equation of "exponential decay", so you can see why taking an antiln is often called "

1. ln (7.42) = ?

2. log (7.42) = ?

3. ln (ekt) = ?

4. log (ekt) = ?

5. antilog 0.8704 = ?

6. antiln 2.0042 = ?

7. 100.8704 = ?

8. e2.0042 = ?

Now do your quiz........

Who understands what forum sections are?Care to explain the rules of this game? And why the heck is this in abrahamic religions???

(I went ahead and moved to the lounge)

Who understands grokking?I'll start:

Who understands what logarithms are?

OK, go!

next!

A person can grok a concept. A person can also grok another person.

Waiting for fullness!

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by 23 and 24 he meant 2^3 and 2^4. Copy and paste can sometimes mess up your format

I was just testing you. Well done. Well done. Splendid.

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Ok I will move it back if warrented, explain yourself.

I think most of us are lost.

We need to know what the title means, vs. the original post, vs. Ok, go.

Title could be Christian, but Abrahamic??

OP looks like either a game or a mathematical question.

As in, "knowing" in the Biblical sense?use a word that was foreign and could simulate the biblical concept of "knowing."

Not to seem impudent, but could a person then correctly say "grok you?"

Not that I am saying this to you, but trying to understand. And enjoying a bit of tongue in cheek fun playing with words.

Who understands Y?

Y is the sky blue?

Y is the sea green?

Y do we even bother?

Y knot?

Y is the sky blue?

Y is the sea green?

Y do we even bother?

Y knot?

Last edited:

I understand X better than anybody, of course.

I understand X better than anybody, of course.

What's this X that people speak of that I should understand?

It's an X thing. You wouldn't understand.