Pc Logarithm Properties
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Properties of Logarithms
MATH PROJECT
LOGARITHIMIC PROPERTIES 1. log a 1 = 0 2. log a a = 1 3. a log a M = M 4. log a a r = r 5. log a ( MN ) = log a M + log a N M 6. log a = log a M − log a N N 7. log a M r = r log a M
( )
1 8. log b = − log b N N 9. log b M = log b N ⇔ M = N
CHANGE OF BASE FORMULA If M, a, and b are positive real numbers with a ≠ 1 and b ≠ 1, then log b M log a M = . log b a
In particular, if M and a are positive real numbers and a ≠ 1, then log M ln M log a M = = . log a ln a
MATH PROJECT
LOGARITHIMIC PROPERTIES 1. log a 1 = 0 2. log a a = 1 3. a log a M = M 4. log a a r = r 5. log a ( MN ) = log a M + log a N M 6. log a = log a M − log a N N 7. log a M r = r log a M
( )
1 8. log b = − log b N N 9. log b M = log b N ⇔ M = N
CHANGE OF BASE FORMULA If M, a, and b are positive real numbers with a ≠ 1 and b ≠ 1, then log b M log a M = . log b a
In particular, if M and a are positive real numbers and a ≠ 1, then log M ln M log a M = = . log a ln a
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