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Today you are going to discover:

2 Patterns of Logs

4 Properties of Logs

1 Formula that will help you evaluate Logs in the calculator!

Pattern #1

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What's the pattern?
Select TWO: the correct "math" and "words" that describe the pattern.
Copy your answers on your paper for Pattern #1.

When the base of the log matches the number inside the log, the log equals 0.

When the base of the log matches the number inside the log, the log equals 1.

When the base of the log matching the number inside the log, the log equals the base.

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Pattern #2

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What's the pattern?
Select TWO: the correct "math" and "words" that describe the pattern.
Copy your answers on your paper for Pattern #2.

Inverse Property

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What is the value of x?

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This one is tricky! It's actually in Exponent form right now, so let's change it into Log form so we can figure out the answer:
What is the answer?

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Notice a pattern from the previous example so you don't need to write out log form every time.

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Same property, but now back to Log form again!

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If the base of the log matches the base of the exponent, they cancel out, and the answer is what's left.

If the base of the log matches the base of the exponent, the answer will always equal the base.

If the base of the log matches the base of the exponent, the answer will always equal 1.

Here's a visual of what's happening in the inverse property:

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Product Property

The product property is used to expand and condense logarithms.

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Expand log(15)
_{*Hint: Any factors of 15 should work.}

When expanding or condensing, always keep the base the same. For example:

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Condense into one logarithm.
_{*Hint: your answer should only have one number inside the log}

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Expand into 3 separate logs.

1

Condense into one logarithm.

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Condense into a single logarithm and evaluate.
_{Hint: your answer should be one number.}

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What is the Product Property?
Select TWO: the correct "math" and correct "words" that describe the property.
Copy your answers on your paper for Product Property.

The log of a product equals the sum of the logs of its factors. (multiply inside = add outside)

The log of a product equals the difference of the logs of its factors. (multiply inside = subtract outside)

The log of a sum equals the product of the logs of its factors. (add inside = multiply outside)

Quotient Property

The quotient property is also used to expand and condense logarithms.

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Expand into two logarithms.

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Condense into one logarithm.

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What is the Quotient Property?
Select TWO: the correct "math" and correct "words" that describe the property.
Copy your answers on your paper for Quotient Property.

The log of a quotient equals the sum of the logs of its divisors. (divide inside = add outside)

The log of a difference equals the quotient of the logs of its factors. (subtract inside = divide outside)

The log of a quotient equals the difference of the logs of its divisors. (divide inside = subtract outside)

Can you apply the product AND quotient properties in the same problem??

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Expand into 3 logarithms.
_{Remember to keep the base 11 on all of the logs in your answer!}

1

Condense into one logarithm.

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Condense into one logarithm and evaluate.
_{Your answer should be one number.}

1

Condense into one logarithm and evaluate.
_{Your answer should be one number.}

Power Property

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Use the power property to expand the logarithm.

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Use the power property to expand the logarithm.

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Use the power property to condense the logarithm.

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What is the Power Property?
Select TWO: the correct "math" and correct "words" that describe the property.
Copy your answers on your paper for Power Property.

The log of a power equals the product of the log and exponent.

The log of a power equals the product of the log and the power.

The log of a power equals the sum of the log and exponent.

The log of a power cancels out the base and equals the exponent.

Can you apply the product AND quotient AND power properties in the same problem??

Example for "expand"

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Expand.

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Expand.

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Condense into a single logarithm.

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Condense into a single logarithm and evaluate.
_{*Your answer should be one number.}

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Condense into a single logarithm and evaluate.
_{*Your answer should be one number.}

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Condense into a single logarithm and evaluate.
_{*Your answer should be one number.}

Change of Base Formula

This formula allows us to evaluate logs in the calculator using the LOG button.

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What is the Change of Base Formula?
Copy your answer on your paper for Change of Base Formula.

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Discover Properties of Logarithms

Pattern #1

Pattern #2

Inverse Property

Product Property

Quotient Property

Power Property

Change of Base Formula

Discover Properties of Logarithms

Today you are going to discover:

2 Patterns of Logs

4 Properties of Logs

1 Formula that will help you evaluate Logs in the calculator!

Pattern #1

What's the pattern?Select TWO: the correct "math" and "words" that describe the pattern.Copy your answers on your paper for Pattern #1.

Pattern #2

What's the pattern?Select TWO: the correct "math" and "words" that describe the pattern.Copy your answers on your paper for Pattern #2.

Inverse Property

What is the value of x?

This one is tricky! It's actually in Exponent form right now, so let's change it into Log form so we can figure out the answer:What is the answer?

Notice a pattern from the previous example so you don't need to write out log form every time.

Same property, but now back to Log form again!

Product Property

Expand log(15)*Hint: Any factors of 15 should work.

Condense into one logarithm.*Hint: your answer should only have one number inside the log

Expand into 3 separate logs.

Condense into one logarithm.

Condense into a single logarithm and evaluate.Hint: your answer should be one number.

What is the Product Property?Select TWO: the correct "math" and correct "words" that describe the property.Copy your answers on your paper for Product Property.

Quotient Property

Expand into two logarithms.

Condense into one logarithm.

What is the Quotient Property?Select TWO: the correct "math" and correct "words" that describe the property.Copy your answers on your paper for Quotient Property.

Can you apply the product AND quotient properties in the same problem??

Expand into 3 logarithms.Remember to keep the base 11 on all of the logs in your answer!

Condense into one logarithm.

Condense into one logarithm and evaluate.Your answer should be one number.

Condense into one logarithm and evaluate.Your answer should be one number.

Power Property

Use the power property to expand the logarithm.

Use the power property to expand the logarithm.

Use the power property to condense the logarithm.

What is the Power Property?Select TWO: the correct "math" and correct "words" that describe the property.Copy your answers on your paper for Power Property.

Can you apply the product AND quotient AND power properties in the same problem??

Expand.

Expand.

Condense into a single logarithm.

Condense into a single logarithm and evaluate.*Your answer should be one number.

Condense into a single logarithm and evaluate.*Your answer should be one number.

Condense into a single logarithm and evaluate.*Your answer should be one number.

Change of Base Formula

What is the Change of Base Formula?Copy your answer on your paper for Change of Base Formula.

Today you are going to discover:

2 Patterns of Logs

4 Properties of Logs

1 Formula that will help you evaluate Logs in the calculator!

What's the pattern?Select TWO: the correct "math" and "words" that describe the pattern.Copy your answers on your paper for Pattern #1.

What's the pattern?Select TWO: the correct "math" and "words" that describe the pattern.Copy your answers on your paper for Pattern #2.

What is the value of x?

This one is tricky! It's actually in Exponent form right now, so let's change it into Log form so we can figure out the answer:What is the answer?

Notice a pattern from the previous example so you don't need to write out log form every time.

Same property, but now back to Log form again!

What is the Inverse Property?Select THREE: two correct "math" examples and one "words" example that describe the property.Copy your answers on your paper for Inverse Property.

Expand log(15)*Hint: Any factors of 15 should work.

Condense into one logarithm.*Hint: your answer should only have one number inside the log

Expand into 3 separate logs.

Condense into one logarithm.

Condense into a single logarithm and evaluate.Hint: your answer should be one number.

What is the Product Property?Select TWO: the correct "math" and correct "words" that describe the property.Copy your answers on your paper for Product Property.

Expand into two logarithms.

Condense into one logarithm.

What is the Quotient Property?Select TWO: the correct "math" and correct "words" that describe the property.Copy your answers on your paper for Quotient Property.

Can you apply the product AND quotient properties in the same problem??

Expand into 3 logarithms.Remember to keep the base 11 on all of the logs in your answer!

Condense into one logarithm.

Condense into one logarithm and evaluate.Your answer should be one number.

Condense into one logarithm and evaluate.Your answer should be one number.

Use the power property to expand the logarithm.

Use the power property to expand the logarithm.

Use the power property to condense the logarithm.

What's the pattern?
Select TWO: the correct "math" and "words" that describe the pattern.
Copy your answers on your paper for Pattern #1.

What's the pattern?
Select TWO: the correct "math" and "words" that describe the pattern.
Copy your answers on your paper for Pattern #2.

This one is tricky! It's actually in Exponent form right now, so let's change it into Log form so we can figure out the answer:
What is the answer?

Expand log(15)
_{*Hint: Any factors of 15 should work.}

Condense into one logarithm.
_{*Hint: your answer should only have one number inside the log}

Condense into a single logarithm and evaluate.
_{Hint: your answer should be one number.}

What is the Product Property?
Select TWO: the correct "math" and correct "words" that describe the property.
Copy your answers on your paper for Product Property.

What is the Quotient Property?
Select TWO: the correct "math" and correct "words" that describe the property.
Copy your answers on your paper for Quotient Property.

Expand into 3 logarithms.
_{Remember to keep the base 11 on all of the logs in your answer!}

Condense into one logarithm and evaluate.
_{Your answer should be one number.}

Condense into one logarithm and evaluate.
_{Your answer should be one number.}

What is the Power Property?
Select TWO: the correct "math" and correct "words" that describe the property.
Copy your answers on your paper for Power Property.

Condense into a single logarithm and evaluate.
_{*Your answer should be one number.}

Condense into a single logarithm and evaluate.
_{*Your answer should be one number.}

Condense into a single logarithm and evaluate.
_{*Your answer should be one number.}

What is the Change of Base Formula?
Copy your answer on your paper for Change of Base Formula.

What's the pattern?
Select TWO: the correct "math" and "words" that describe the pattern.
Copy your answers on your paper for Pattern #1.

What's the pattern?
Select TWO: the correct "math" and "words" that describe the pattern.
Copy your answers on your paper for Pattern #2.

This one is tricky! It's actually in Exponent form right now, so let's change it into Log form so we can figure out the answer:
What is the answer?

What is the Inverse Property?
Select THREE: two correct "math" examples and one "words" example that describe the property.
Copy your answers on your paper for Inverse Property.

Expand log(15)
_{*Hint: Any factors of 15 should work.}

Condense into one logarithm.
_{*Hint: your answer should only have one number inside the log}

Condense into a single logarithm and evaluate.
_{Hint: your answer should be one number.}

What is the Product Property?
Select TWO: the correct "math" and correct "words" that describe the property.
Copy your answers on your paper for Product Property.

What is the Quotient Property?
Select TWO: the correct "math" and correct "words" that describe the property.
Copy your answers on your paper for Quotient Property.

Expand into 3 logarithms.
_{Remember to keep the base 11 on all of the logs in your answer!}

Condense into one logarithm and evaluate.
_{Your answer should be one number.}

Condense into one logarithm and evaluate.
_{Your answer should be one number.}

What is the Power Property?
Select TWO: the correct "math" and correct "words" that describe the property.
Copy your answers on your paper for Power Property.

Condense into a single logarithm and evaluate.
_{*Your answer should be one number.}

Condense into a single logarithm and evaluate.
_{*Your answer should be one number.}

Condense into a single logarithm and evaluate.
_{*Your answer should be one number.}

What is the Change of Base Formula?
Copy your answer on your paper for Change of Base Formula.