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MATH REVIEW: USEFUL MATH FOR EVERYONESECTION 4.4. WHAT IS A LOGARITHM? 4. log (P*Q) = log P + log Q means that if you take the logarithm of two factors, it is the same as taking the logarithm of each factor, and adding them together. For example:
If you were using natural logarithms, it would look like this:
(Note that the numerical value of the natural logarithm is different from that of the base ten logarithm. That's because, in the second example, 1.792 is the power to which 'e' must be raised to get 6, whereas, in the first example, 0.778 is the power to which 10 must be raised to get 6.) If you have a variable as one of your factors, it would look like this:
Let's say log 2y = 36 and solve for y:
which is a really big number.
5. log (P/Q) = log P - log Q means that if you take a logarithm of one number divided by another, it is the same as taking each logarithm separately, and then subtracting the logarithm of the denominator from the logarithm of the numerator. For example:
If you were using natural logarithms, it would look like this:
If you have a variable as one of your factors, it would look like this:
Let's say log (y/2) = 36 and solve for y:
which is an even bigger number.
6. log (Pt) = t * log P means that the logarithm of a number raised to some power, it is the same as multiplying the logarithm of that number by the value of the power. For example:
It looks the same when you use natural logarithms, however, as in example three the numerical value will be different.
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