Here are the properties of logarithms demonstrated by each equation:
1)
Product Property
(Because adding logs with the same base equals the log of the product: $\log_b x + \log_b y = \log_b(xy)$)
2)
Quotient Property
(Because subtracting logs with the same base equals the log of the quotient: $\log_b x - \log_b y = \log_b(\frac{x}{y})$)
3)
Power Property
(Because moving an exponent from inside the log to the front as a multiplier: $\log_b(x^n) = n \log_b x$)
4)
Product Property
(Same reason as #1: $5 \times 25 = 125$, so $\log_5 5 + \log_5 25 = \log_5(5 \cdot 25) = \log_5 125$)
5)
Quotient Property
(Same reason as #2: $\log_3 2 - \log_3 3 = \log_3(\frac{2}{3})$)
6)
Power Property
(Same reason as #3: The coefficient 2 becomes the exponent on the argument: $2 \log 4 = \log(4^2)$)
7)
c) Power Property
(The exponent 3 is moved from the power position to become a coefficient in front of the log.)
8)
b) Quotient Property
(Subtracting two logs results in the log of their division/fraction.)
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Final Answer:
1) Product Property
2) Quotient Property
3) Power Property
4) Product Property
5) Quotient Property
6) Power Property
7) c) Power Property
8) b) Quotient Property
Parent Tip: Review the logic above to help your child master the concept of algebra 2 properties of logarithms worksheet.
