document.write( "Question 152408: Hi, my name is Stormy i'm going into 9th grade and I start Wednesday.I have no clue what the logarithm is and i would like too know so that i have a headstart in algebra concept this year. I get all a's and don't want them to drop. This is the first year i did not attend summer school and they learned the logarithm this year. if you could please give me a short explanation of what the logarithm is i would greatly appreciate it.
\n" ); document.write( " Thanks again,
\n" ); document.write( " Stormy \n" ); document.write( "
Algebra.Com's Answer #112016 by Earlsdon(6294)\"\" \"About 
You can put this solution on YOUR website!
You are not alone in being mystified by logarithms!
\n" ); document.write( "To understand logarithms, you should be familiar with exponents because they are closely related.
\n" ); document.write( "Remember exponents, also called powers?
\n" ); document.write( "\"10%5E2+=+100\" Here, the base is 10 and the exponent (power) is 2.
\n" ); document.write( "\"2%5E3+=+8\" Here, the base is 2 and the exponent is 3.
\n" ); document.write( "So, here's a definition of logarithms:
\n" ); document.write( "\" The logarithm of a number is the power to which the base of the logarithm must be raised to equal the number\"
\n" ); document.write( "So a logarithm has a \"base\".
\n" ); document.write( "Commonly, this base is 10, but it can be any number. When the logarithm has a base of 10, it is called a \"common logarithm\" or \"common log\" for short.
\n" ); document.write( "Let's see how this works:
\n" ); document.write( "Let's suppose that we want to find the common log (base 10) of 100.
\n" ); document.write( "We would write:
\n" ); document.write( "\"log%28100%29+=+x\" You could show the base if you wanted to make absolutely sure that your reader undertood which base you were using by:
\n" ); document.write( "\"Log%5B10%5D%28100%29+=+x\" but, if no base is shown, and the notation is log or Log, then common logarithms are assumed.
\n" ); document.write( "What the above equation says is...\"x is the power to which the base (10) must be raised to equal 100\".
\n" ); document.write( "Well, you know that already because \"10%5E2+=+100\" so x must equal 2, or
\n" ); document.write( "\"Log%5B10%5D+%28100%29+=+2\"
\n" ); document.write( "In fact, you can express the logarithm above in exponential a general form:
\n" ); document.write( "\"b%5Ex+=+100\" The base (b) is 10 and x = 2, so...
\n" ); document.write( "\"10%5E2+=+100\"
\n" ); document.write( "In more general terms, let b denote the base, we can write:
\n" ); document.write( "\"Log%5Bb%5D%28x%29+=+y\" You would read this as: \"The log, to the base b, of x = y\" and this can be expressed in exponential form as:
\n" ); document.write( "\"b%5Ey+=+x\"
\n" ); document.write( "Let's try a few more numbers, but we will stay with common (base 10) logs for now.
\n" ); document.write( "\"Log%281000%29+=+3\" why, because \"10%5E3+=+1000\"
\n" ); document.write( "\"Log%2810%29+=+1\" why, because \"10%5E1+=+10\"
\n" ); document.write( "Now if you wanted to find the common log of a number that is not a multiple of the base (10), you would then have to resort to a calculator or a table of common logarithms.
\n" ); document.write( "For example:
\n" ); document.write( "\"log%283%29+=+0.47712125\" approximately. The result is an irrational number (remember those?)
\n" ); document.write( "Most scientific or math calculators will have a logarithm key.
\n" ); document.write( "This is just an overview but you could log on to any good information site and type in Logarithms and you'd probably get more information on the topic than you could use.
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