| You could ask the question: | ||
| "What exponent do you have to raise 5 to, to get 125?" | ||
| and most everybody would know what you meant and be perfectly happy. | ||
| Everyone that is, EXCEPT math types. | ||
| Math people wanted a way to write stuff like that in a few numbers and symbols. | ||
| They got one. What they came up with was the word "log." | ||
| A kind of funny word for math eh? | ||
| Well who knows why they chose it, but what it means is ... | ||
| "The exponent that you have to raise" | ||
| after it you write a small number and then a regular size number. | ||
| The small number is the number you multiply times itself. | ||
| The big number is the answer you get when you do the multiplying. | ||
| It goes together like this: | ||
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|
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SO WHAT IS THE EXPONENT 5 MUST BE RAISED TO TO GET 125? |
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|
||
| So ... | ||
|
log5125 = 3 |
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| The way you SAY this thing in English goes like this: | ||
| Fancy way: The log, base 5 of 125 equals 3. | ||
| Less fancy way: log 5 of 125 is 3. | ||
|
|
||
| But it means: The exponent that 5 must be raised to, to get 125 is 3. | ||
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| Always, always, always read the meaning when you look at logs. | ||
| The little number after the word log is called the base. | ||
| It is very important. | ||
| In ancient times (before 1980) the only easy way | ||
| to find the value of something like: | ||
|
log4256 |
||
| was to try to look it up in a table of logs in a book. | ||
| These tables are lists of logs that were printed | ||
| in the back of many math books. | ||
| Usually, the tables were only printed for two different bases. | ||
| Base 10 and another special base called e. | ||
| We'll talk about the e thing some other time. | ||
| Base 10 logs are used a bunch. | ||
| They are used so much that when we write them, | ||
| we can leave the base number out. | ||
| Like this ... | ||
|
log10200 = log 200 |
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| So if you see: | ||
|
log 1000 |
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| It means: | ||
|
log101000 |
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| And what does log101000 mean? | ||
| ALL TOGETHER NOW: | ||
|
THE EXPONENT THAT YOU HAVE TO RAISE 10 TO, |
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TO GET 1000 |
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| Example: | ||
| OK, What if we have ... | ||
|
log55 = ? |
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| What's the answer? | ||
| Just read the meaning, | ||
| it means: | ||
|
THE EXPONENT THAT YOU HAVE TO RAISE 5 TO, |
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|
TO GET 5 |
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| Well: | ||
|
51 = 5 so log55 = 1 |
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| Example: | ||
| How about ... | ||
|
log31 = ? |
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| It means ... | ||
|
THE EXPONENT THAT YOU HAVE TO RAISE 3 TO, |
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|
TO GET 1 |
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| The special rule says: | ||
|
30 = 1 |
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| So ... | ||
|
log31 = 0 |
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| Example: | ||
| OK, Try this ... | ||
|
log12-10 = ? |
||
| It means ... | ||
| THE EXPONENT THAT YOU HAVE TO RAISE 12 TO, | ||
| TO GET -10. | ||
| Well you can multiply 12's together till the end of time | ||
| and it will NEVER get a negative number for an answer. | ||
| So this one has no answer. | ||
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| Example: | ||
| Here's a very nasty one ... | ||
|
7log7500 = ? |
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| What does this equal? | ||
| OK, don't panic, just read it. | ||
| You might get a surprise: | ||
| Seven, raised to | ||
| THE EXPONENT THAT YOU HAVE TO RAISE 7 TO, TO GET 500. | ||
| So what do you get | ||
| when you raise 7 to the exponent that you have to raise 7 to, to get 500? | ||
|
YOU GET 500! |
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|
7log7500 = 500 |
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| But don't you need to find out what the exponent number is? | ||
| NOPE! | ||
| Hey, if they don't ask for it, why do it? | ||
|
copyright 2005 Bruce Kirkpatrick |
