Logarithms

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

This math topic focuses on using the logarithmic product property to convert products within logarithmic expressions into sums of logarithms, specifically applying integer multiplication. The practice involves rewriting expressions such as \(\log_b(a \cdot c)\) into the sum form \(\log_b a + \log_b c\). For instance, if tasked with rewriting \(\log_5(9 \times 2)\), the correct form would be \(\log_5 9 + \log_5 2\), emphasizing the understanding of basic logarithmic laws in various contexts, such as real-world applications or further mathematical operations. This forms an integral part of introductory studies on logarithm functions.

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

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Logarithms - Product Property - Product to Sum (Integer Multiplication) Worksheet

Logarithms - Product Property - Product to Sum (Integer Multiplicatio...

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

$A LaTex expression showing \log sub 5 (9 times 2)$

a $A LaTex expression showing \log sub 2 9 + \log sub 2 5$

b $A LaTex expression showing \log sub 9 2 + \log sub 9 5$

c $A LaTex expression showing \log sub 9 5 + \log sub 9 2$

d $A LaTex expression showing \log sub 5 9 + \log sub 5 2$

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

$A LaTex expression showing \log sub 8 (3 times 9)$

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

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

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

d $A LaTex expression showing \log sub 8 11 + \log sub 8 7$

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

$A LaTex expression showing \log sub 5 (4 times 6)$

a $A LaTex expression showing \log sub 4 5 + \log sub 4 6$

b $A LaTex expression showing \log sub 5 4 + \log sub 5 6$

c $A LaTex expression showing \log sub 4 6 + \log sub 4 5$

d $A LaTex expression showing \log sub 6 4 + \log sub 6 5$

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

$A LaTex expression showing \log sub 9 (7 times 3)$

a $A LaTex expression showing \log sub 9 7 + \log sub 9 3$

b $A LaTex expression showing \log sub 7 9 + \log sub 7 3$

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

d $A LaTex expression showing \log sub 7 3 + \log sub 7 9$

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

$A LaTex expression showing \log sub 6 (4 times 10)$

a $A LaTex expression showing \log sub 4 10 + \log sub 4 6$

b $A LaTex expression showing \log sub 6 4 + \log sub 6 10$

c $A LaTex expression showing \log sub 6 13 + \log sub 6 7$

d $A LaTex expression showing \log sub 10 4 + \log sub 10 6$

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

$A LaTex expression showing \log sub 10 (4 times 5)$

a $A LaTex expression showing \log sub 4 10 + \log sub 4 5$

b $A LaTex expression showing \log sub 4 5 + \log sub 4 10$

c $A LaTex expression showing \log sub 10 4 + \log sub 10 5$

d $A LaTex expression showing \log sub 5 4 + \log sub 5 10$

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

$A LaTex expression showing \log sub 8 (10 times 4)$

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

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

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

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

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

$A LaTex expression showing \log sub 8 (3 times 4)$

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

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

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

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