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

Math worksheet on 'Logarithms - Product Property - To Sum (Level 1)'. Part of a broader unit on 'Logarithm Functions - Intro' Learn online: app.mobius.academy/math/units/logarithms_functions_intro/

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

$A LaTex expression showing \log sub 6 30$

a $A LaTex expression showing \log sub 10 6 + \log sub 10 3$

b $A LaTex expression showing \log sub 3 10 + \log sub 3 6$

c $A LaTex expression showing \log sub 6 7 + \log sub 6 14$

d $A LaTex expression showing \log sub 6 10 + \log sub 6 3$

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

$A LaTex expression showing \log sub 3 72$

a $A LaTex expression showing \log sub 8 9 + \log sub 8 3$

b $A LaTex expression showing \log sub 3 9 + \log sub 3 8$

c $A LaTex expression showing \log sub 3 12 + \log sub 3 13$

d $A LaTex expression showing \log sub 3 11 + \log sub 3 12$

e $A LaTex expression showing \log sub 9 8 + \log sub 9 3$

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

$A LaTex expression showing \log sub 3 12$

a $A LaTex expression showing \log sub 3 8 + \log sub 3 5$

b $A LaTex expression showing \log sub 3 8 + \log sub 3 4$

c $A LaTex expression showing \log sub 2 3 + \log sub 2 6$

d $A LaTex expression showing \log sub 3 2 + \log sub 3 6$

e $A LaTex expression showing \log sub 2 6 + \log sub 2 3$

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

$A LaTex expression showing \log sub 7 18$

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

b $A LaTex expression showing \log sub 7 3 + \log sub 7 6$

c $A LaTex expression showing \log sub 6 3 + \log sub 6 7$

d $A LaTex expression showing \log sub 3 6 + \log sub 3 7$

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

$A LaTex expression showing \log sub 5 32$

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

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

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

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

e $A LaTex expression showing \log sub 5 7 + \log sub 5 12$

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

$A LaTex expression showing \log sub 2 10$

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

b $A LaTex expression showing \log sub 2 7 + \log sub 2 5$

c $A LaTex expression showing \log sub 2 8 + \log sub 2 5$

d $A LaTex expression showing \log sub 2 5 + \log sub 2 2$

e $A LaTex expression showing \log sub 2 9 + \log sub 2 6$

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

$A LaTex expression showing \log sub 6 18$

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

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

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