Logarithms - Product Property - To Sum (Level 1) - Mobius Math Academy

Product Property - To Sum (Level 1)

This math topic is focused on practicing the product property of logarithms, specifically converting a given logarithmic expression into a sum of logarithms. Students utilize the logarithmic rule stating that the logarithm of a product is the sum of the logarithms of the factors: \(\log_b(xy) = \log_b(x) + \log_b(y)\). Each question provides a logarithmic expression and multiple potential answers, where the correct application of the product property must be selected. This topic is part of a broader unit on logarithms and aids in enhancing understanding of logarithmic relationships and operations.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Logarithms - Product Property - To Sum Worksheet

Logarithms - Product Property - To Sum

Convert the given logarithm to its equivalent based on the product property

$A LaTex expression showing \log sub 3 45$

a $A LaTex expression showing \log sub 5 9 + \log sub 5 3$

b $A LaTex expression showing \log sub 3 9 + \log sub 3 12$

c $A LaTex expression showing \log sub 3 8 + \log sub 3 13$

d $A LaTex expression showing \log sub 3 9 + \log sub 3 5$

Convert the given logarithm to its equivalent based on the product property

$A LaTex expression showing \log sub 9 36$

a $A LaTex expression showing \log sub 9 11 + \log sub 9 7$

b $A LaTex expression showing \log sub 9 12 + \log sub 9 8$

c $A LaTex expression showing \log sub 9 11 + \log sub 9 6$

d $A LaTex expression showing \log sub 9 11 + \log sub 9 8$

e $A LaTex expression showing \log sub 9 4 + \log sub 9 9$

Convert the given logarithm to its equivalent based on the product property

$A LaTex expression showing \log sub 7 32$

a $A LaTex expression showing \log sub 8 4 + \log sub 8 7$

b $A LaTex expression showing \log sub 4 8 + \log sub 4 7$

c $A LaTex expression showing \log sub 7 8 + \log sub 7 4$

d $A LaTex expression showing \log sub 8 7 + \log sub 8 4$

Convert the given logarithm to its equivalent based on the product property

$A LaTex expression showing \log sub 5 8$

a $A LaTex expression showing \log sub 5 4 + \log sub 5 2$

b $A LaTex expression showing \log sub 5 4 + \log sub 5 8$

c $A LaTex expression showing \log sub 2 4 + \log sub 2 5$

d $A LaTex expression showing \log sub 5 4 + \log sub 5 7$

Convert the given logarithm to its equivalent based on the product property

$A LaTex expression showing \log sub 7 15$

a $A LaTex expression showing \log sub 7 5 + \log sub 7 9$

b $A LaTex expression showing \log sub 5 7 + \log sub 5 3$

c $A LaTex expression showing \log sub 7 7 + \log sub 7 9$

d $A LaTex expression showing \log sub 7 5 + \log sub 7 3$

e $A LaTex expression showing \log sub 3 5 + \log sub 3 7$

Convert the given logarithm to its equivalent based on the product property

$A LaTex expression showing \log sub 5 21$

a $A LaTex expression showing \log sub 5 7 + \log sub 5 3$

b $A LaTex expression showing \log sub 7 5 + \log sub 7 3$

c $A LaTex expression showing \log sub 5 7 + \log sub 5 10$

d $A LaTex expression showing \log sub 3 7 + \log sub 3 5$

Convert the given logarithm to its equivalent based on the product property

$A LaTex expression showing \log sub 6 18$

a $A LaTex expression showing \log sub 6 6 + \log sub 6 3$

b $A LaTex expression showing \log sub 3 6 + \log sub 3 6$

c $A LaTex expression showing \log sub 6 3 + \log sub 6 6$

Convert the given logarithm to its equivalent based on the product property

$A LaTex expression showing \log sub 4 80$

a $A LaTex expression showing \log sub 4 10 + \log sub 4 12$

b $A LaTex expression showing \log sub 4 10 + \log sub 4 8$

c $A LaTex expression showing \log sub 10 8 + \log sub 10 4$

d $A LaTex expression showing \log sub 10 4 + \log sub 10 8$