If you know that 2 raised to the 3 power is 8 then you know a logarithm,
The fill-in-the-blank problem:
= ___
amounts to the following fill-in-the-blank problem.
2 raised to the ___ power is 8.
In both cases the number that goes in the blank is 3.
In other words, a logarithm IS the exponent to which we must raise the
base in order get the number that we are taking the log of.
Since that means that
Since that means that
Since that means that
Since that means that
Since that means that
Since that means that
Remember
1. The base of the exponent equals the base of the log.
2. The log equals the exponent
3. The result of the exponentiating is what the log is taken of.
Edwin
You can put this solution on YOUR website! Logarithm is an unfortunate name for what is actually the exponent.
eg:
so log(100) = 2 --- the exponent is 2. so --- 4 is the exponent.
Often just explaining that logarithm is actually the exponent makes it much clearer.
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As for finding it, most calculators have a Log button for "common logs", which is base 10. The log is the exponent that 10 is raised to to get the number, or argument.
Most also have a natural log button, ln, which is base e. More about that later.
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If you need to find a log with some other base, use the base change method, eg,
That'll give the the exponent which will raise the base (5) to be 66.
