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2.4 LOGARITHMS
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The use of logarithms is a fast method of finding an unknown exponent.
Section 7.4
Base Exponent
9 = 81?
3 = 27?2 = 16
Logarithm and its Relation to Exponents
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The use of logarithms is a fast method of finding an unknown exponent.
Section 7.4
How can we calculate this?
log 819
= log 27
3=
log 1007
=
Logarithm and its Relation to Exponents
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The logarithm of a number is the exponent by which a fixed number , the base, has to be raised to produce that number.
Section 7.4
ax = yBase
Exponent
Number
log
ya x= Base Number
Logarithm(Exponent)
Exponential form
Logarithmic form
Logarithm and its Relation to Exponents
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The logarithm of a number is the exponent by which a fixed number , the base, has to be raised to produce that number.
Section 7.4
43 = 64
54 = 625
Logarithm and its Relation to Exponents
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Most calculators can only solve for two special kinds of logarithms,the Common Logarithm (log) and the Natural Logarithm (ln).
Section 7.4
102 = 100
Common Logarithms and Natural Logarithms
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Most calculators can only solve for two special kinds of logarithms,the Common Logarithm (log) and the Natural Logarithm (ln).
Section 7.4
log 1 = 0log 10 = 1
log 100 = 2log 1000 = 3
Common Logarithms and Natural Logarithms
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Business calculators can only solve for the Natural Logarithm (ln), pronounced “lawn”. ln is to the base e, which is a special number.
Section 7.4
Natural logarithm
button
Common Logarithms and Natural Logarithms
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Business calculators can only solve for the Natural Logarithm (ln), pronounced “lawn”. ln is to the base e, which is a special number.
Section 7.4
e2 = 7.39 log 7.39e
= 2
ln7.39 = 2A logarithm to the base of e is called the natural logarithm.
It is abbreviated as “ln”, without writing the base.
Simply “ln” without a
base implies log .e
e = 2.718282
Common Logarithms and Natural Logarithms
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Business calculators can only solve for the Natural Logarithm (ln), pronounced “lawn”. ln is to the base e, which is a special number.
Section 7.4
ln 1 = 0ln e = 1
ln10 = 2.302585…ln1000 = 6.907755…
Common Logarithms and Natural Logarithms
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Common logarithms (log) and natural logarithms (ln) follow the same rules.
Section 7.4
Product Rule
ln AB = ln A + ln B
ln (2×3) =ln (15×25) =
Rules of Logarithms
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Common logarithms (log) and natural logarithms (ln) follow the same rules.
Section 7.4
Quotient Rule
= ln A − ln B ln AB ( )
=ln 32( )
=ln 2712( )
Rules of Logarithms
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Common logarithms (log) and natural logarithms (ln) follow the same rules.
Section 7.4
Power Rule
ln (A)n = nln A
ln (10)2 =
ln (67)4 =
Rules of Logarithms
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Common logarithms (log) and natural logarithms (ln) follow the same rules.
Section 7.4
0 as a power or 1 as logarithm
ln (A)0 = ln 1 = 0
ln (15)0 =
ln (32)0 =
Rules of Logarithms
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Solution
4n = 65,536
Solve for “n” in the following equation.
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Solution
Solve for “n” in the equation 36(2)n = 147,456.
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