Discover Properties of Logarithms

Today you are going to discover:
Patterns of Logs
Properties of Logs
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.

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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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.

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

Product Property
The product property is used to expand and condense logarithms.

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Use your calculator to evaluate the following. Round all answers to the nearest tenth.

log(16)=_______ 
log(8⋅2)=_______ 
log(8)+log(2)=_______ 

Therefore, we can expand log(8⋅2) to log(8)+log(2) without changing the value of the logarithm.

Expand log(6⋅3)=_______ <- type out the logs, not a decimal
Expand log(4⋅x)=_______ <- type out the logs, not a decimal

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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.

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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.

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

1

Use your calculator to evaluate the following. Round all answers to the nearest tenth.

log(16)=_______ 
log(32\div 2)=_______ 
log(32)-log(2)=_______ 

Therefore, we can expand log(32/2) to log(32)-log(2) without changing the value of the logarithm.

Expand log(6\div3)=_______ <- write out two logs, not a decimal
Expand log(4/x)=_______ <- write out two logs, not a decimal

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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.

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!

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Condense into one logarithm.

1

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

1

Use your calculator to evaluate the following. Round all answers to the nearest tenth.

log(25)=_______ 
log(5^2)=_______ 
2\cdot log(5)=_______ 

Therefore, when taking the log of a power, we can bring the exponent down infront of the log without changing the value of the logarithm: 

Use the power property to expand log(6^3)=_______ 
Use the power property to expand log(7^x)= _______ 

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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.

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.

1

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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Use your calculator to evaluate the following. Round all answers to the nearest tenth.
\log _{10}\left(40\right)=_______ 

\frac{\log \left(40\right)}{\log \left(10\right)}=_______ 

Therefore, when evaluating a log, we can divide the log of the inside number by the log of the base without changing the value of the logarithm. This will work for any base, but it makes sense for us to use  \log _{10} or ln since that is on our calculators.

Change of Base Examples:

Use the change of base formula to evaluate in the calculator:
 \log _{4}\left(85\right)=_______ 
\log _{16}\left(64\right)= _______

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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!

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.

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

Change of Base Examples:

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!

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!

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.

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.

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.

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.