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)= _______
Question 50
50.
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.
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.
What's the pattern?
Select TWO: the correct "math" and "words" that describe the pattern.
Copy your answers on your paper for Pattern #2.
The log of 1 will always equal the base.
The log of 1 will always equal 0.
The log of 1 will always equals 1.
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.
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.
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)
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)
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.