Exponent and Logarithm Math
There are a number of times when working with various equations that we run into situations where we need to use logarithms and exponents. If we're trying to solve an equation for a variable that is an exponent, we can use the properties of logarithms to solve the equation for that variable. If we keep a few rules in mind, logarithms and exponents can be very powerful tools.
Natural Log vs. Common Log:
Any logarithm is just the power (exponent) to which a base is raised to get a certain value. Natural log is the power to which you raise the value "e" (equal to approximately 2.71828); a common log is a power of 10. Log math works the same for either type of logarithm, the only difference is the base number. Also, a log and its base are the inverse of each other so:
ln (ex) = x
eln(x) = x
log (10x) = x
10log(x) = x
Now that we know what logs are, how do we treat them in an equation?
Log Multiplication:
The log of a product is equal to the sum of the log of each term.
log (AB) = log (A) + log (B)
Log Division:
The log of a fraction is equal to the log of the numerator minus the log of the denominator.
log (A/B) = log (A) - log (B)
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Last updated 01/05/2005
by JBodwin
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