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In precalculus, exponents and logarithms are used extensively. These topics are important to learn if calculus and other math subjects are to be studied.
This page shows most of the rules used in precalculus for exponents and logarithms and how they are related. The rules for exponents are related to the rules for logarithms by the master rule.
ln is used to represent a logarithm of base e which is the natural number. The natural number is roughly equal to 2.71828.
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The Master Rule of logarithms and exponents
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logab = x ↔ ax = b
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Rules of exponents:
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1. a0 = 1
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2. a1 = a
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2. a1 = a
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3. eln(b) = b
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4. ex+y = exey
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7. (ab)x = axbx
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9. axy = (ax)y
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10. a1/x = x√a
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11. ax/y = y√ax
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Rules of logarithms:
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1. loga1 = 0
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2. logaa = 1
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3. logaax = x
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4. logabx = xlogab
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5. loga(bc) = logab + logac
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6.
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loga
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(
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b
c
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)
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=
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logab − logac
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8.
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logax√b
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=
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(
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1
x
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)
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logab
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9.
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logax√by
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=
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(
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y
x
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)
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logab
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