 Log of Both Sides Theorem
If A, B, and b are positive real numbers
with b not equal to 1, then
log_{b}A = log_{b}B
is equivalent to A = b.
 Logarithmic Equations
Log Type I: The unknown is the logarithm.
Log Type II: The unknown is the base.
Log Type III: The logarithm of an unknown is
equal to a number.
Log Type IV: The logarithm of an unknown is equal
to the logarithm of a number.  Laws of Logarithms
Let A, B, and b be positive numbers
(b not equal to 1) and let p be any real number,
First law (Additive):
log_{b}(AB) = log_{b}A + log_{b}B
Second law (Subtractive):
log_{b}(A/B) = log_{b}A
+ log_{b}B
Third law (Multiplicative):
log_{b}(A)^{p}
= P log_{b}A
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© 2011 Karl J. Smith. All rights reserved. 