Logarithms

Product Property - Sum to Product as Integer (Level 1)

This topic focuses on practicing the application of the product property in logarithms to convert the sum of logarithms into a single logarithmic expression. The problems require converting expressions like "\(\log_b x + \log_b y\)" into the form "\(\log_b (xy)\)", where \(b\) is the base of the logarithm. Each question provides a different log expression and options for the correct transformation according to the product property. In solving these problems, students solidify their understanding of logarithmic identities and rules essential for algebraic manipulation and simplification of logarithmic expressions.

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

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Logarithms - Product Property - Sum to Product as Integer Worksheet

Logarithms - Product Property - Sum to Product as Integer

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

$A LaTex expression showing \log sub 8 9 + \log sub 8 5$

a $A LaTex expression showing \log sub 9 45$

b $A LaTex expression showing \log sub 45 8$

c $A LaTex expression showing \log sub 8 45$

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

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

a $A LaTex expression showing \log sub 15 9$

b $A LaTex expression showing \log sub 9 14$

c $A LaTex expression showing \log sub 9 17$

d $A LaTex expression showing \log sub 9 15$

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

$A LaTex expression showing \log sub 3 4 + \log sub 3 7$

a $A LaTex expression showing \log sub 3 28$

b $A LaTex expression showing \log sub 3 26$

c $A LaTex expression showing \log sub 28 3$

d $A LaTex expression showing \log sub 3 29$

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

$A LaTex expression showing \log sub 2 9 + \log sub 2 7$

a $A LaTex expression showing \log sub 63 2$

b $A LaTex expression showing \log sub 2 63$

c $A LaTex expression showing \log sub 2 62$

d $A LaTex expression showing \log sub 2 64$

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

$A LaTex expression showing \log sub 2 9 + \log sub 2 3$

a $A LaTex expression showing \log sub 2 27$

b $A LaTex expression showing \log sub 27 2$

c $A LaTex expression showing \log sub 0 27$

d $A LaTex expression showing \log sub 2 26$

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

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

a $A LaTex expression showing \log sub 8 15$

b $A LaTex expression showing \log sub 7 13$

c $A LaTex expression showing \log sub 15 7$

d $A LaTex expression showing \log sub 7 15$

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

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

a $A LaTex expression showing \log sub 6 19$

b $A LaTex expression showing \log sub 6 20$

c $A LaTex expression showing \log sub 6 18$

d $A LaTex expression showing \log sub 6 16$

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

$A LaTex expression showing \log sub 7 3 + \log sub 7 10$

a $A LaTex expression showing \log sub 7 30$

b $A LaTex expression showing \log sub 7 31$

c $A LaTex expression showing \log sub 30 7$

d $A LaTex expression showing \log sub 7 29$