Logarithm rules

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Logarithm rules

• Section 5.4

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Worksheet
Logarithm rules worksheet derives the formulas
given in section 5.4. If we can think through the
formulas, they will be easier to memorize and
apply. Well do 2 from the worksheet as an
introduction. In words, what is ? Its the
number to which I raise _____ to get _____. What
does this number we call have to
be? First, its the number to which I raise b to
get 1. Since if you raise any number to 0, you
get 1, we know
3

• Now that Logarithm rules worksheet" has
  introduced the rules we need, we will learn to
  manipulate logs. Mostly, we are practicing this
  manipulation so we can solve equations in the
  next section.
• We will sometimes need the Change of Base
  Formula.
• Remember we cannot do logs other than 10 or e on
  our calculators, so we need a way to find and
  the like.

Whatever the base is, you can rewrite it in terms
of either base 10 or base e logs.
or
4
expl
Notice this works since
We could have also done

• For the following problems, we will need a few
  rules from the Logarithm rules worksheet.

5
expl 29
1. 2. 3.

• Write as a single logarithm.

Well simplify the first term by using rule 3
and further simplify the exponent. Then well use
rule 1 to combine terms 2 and 3, and rule 2 to
combine the remaining terms.
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Rule 3 here
Rule 1 here
Divide by a fraction, multiply by its reciprocal.
Rule 2 here
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expl 18
1. 2. 3.

• Write as a sum and/or difference of logs. Express
  powers as factors.

Well use rule 1 to break apart the fraction.
Then well use rule 2 to break apart the first
term. Finally, well use rule 3 to simplify each
term.
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Rule 1 here
Rule 2 here
Rule 3 here
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expl 12

• Write in terms of a and b where and .

Change of base formula
You are told that and
10
expl 36
Remember rules of exponents!

• Find exact value.

is the number to which I raise 5 to get
6. Then 5 raised to this number ( ) must be 6.
Similarly,
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• Concerning 35 in homework This is similar to
  36.
• Recall the rules of exponents like .

Do 5.4 homework after Logarithm rules
worksheet. 5.4 homework 1, 2, 5, 11, 13, 17,
25, 30, 35, 39, 47 Numbers 11, 39, and 47
involve the Change of Base formula.