A logarithm (of the base b) is the power to which the base needs to be raised to yield a given number.

 

If x equals b raised to the power of y,

 

x=b^y

 

then the log of x (base b) equals y.

 

log_b(x)=y

 

 

So, for example, using a base of 10 (log₁₀ or log base 10), the logarithm of 1,000 equals 3 because 10 raised to the three equals 1,000.

 

If 10 raised to the power of three equals 1,000,

 

10³=1,000

 

then the log (base 10) of 1,000 equals 3.

 

log₁₀1000=3

 

The natural logarithm is one of the most commonly used logs in statistics. This logarithm has the constant e as its base ( e = approximately 2.718281828459…).    The definite integral of 1 to e of 1/x dx equals one (you don’t need to remember that, just one of the elegant gems of mathematics!!!).   The natural log is often written ln(x) and is equivalent to log_e(x).  Now it’s time for the log rules.

 

The Log Rules!!!

 

To manipulate logarithms, you should understand and be able to apply the following rules.  Remember that ln = log base e (log_e).

 

Go to the page on Factorials!!

 

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This website was developed by Elizabeth A. Albright, PhD of the Nicholas School of the Environment, Duke University. Follow Elizabeth A. Albright, PhD on Twitter @enviro_prof.

 

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