Logarithms

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

This math topic focuses on practicing the logarithmic product property, which converts the logarithm of a product into the sum of logarithms. The problems require converting a single logarithmic expression into a sum of two logarithms that represent the factors of the original integer inside the logarithm's argument. This is an introductory session to logarithm functions, and it is designed for learners to understand and apply the product property of logarithms effectively. The topic features multiple-choice questions where students must recognize the correct application of the product property to given logarithmic expressions.

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

more

Worksheet ViewUnit

Logarithms - Product Property - Product as Integer To Sum Worksheet

Logarithms - Product Property - Product as Integer To Sum

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

$A LaTex expression showing \log sub 7 10$

a $A LaTex expression showing \log sub 7 7 + \log sub 7 6$

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

c $A LaTex expression showing \log sub 7 9 + \log sub 7 6$

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

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

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

$A LaTex expression showing \log sub 7 72$

a $A LaTex expression showing \log sub 8 9 + \log sub 8 7$

b $A LaTex expression showing \log sub 7 11 + \log sub 7 10$

c $A LaTex expression showing \log sub 7 8 + \log sub 7 9$

d $A LaTex expression showing \log sub 8 7 + \log sub 8 9$

e $A LaTex expression showing \log sub 7 11 + \log sub 7 12$

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

$A LaTex expression showing \log sub 8 20$

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

b $A LaTex expression showing \log sub 8 7 + \log sub 8 6$

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

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

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

$A LaTex expression showing \log sub 5 24$

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

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

c $A LaTex expression showing \log sub 5 6 + \log sub 5 10$

d $A LaTex expression showing \log sub 5 6 + \log sub 5 8$

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

$A LaTex expression showing \log sub 6 20$

a $A LaTex expression showing \log sub 6 4 + \log sub 6 13$

b $A LaTex expression showing \log sub 10 2 + \log sub 10 6$

c $A LaTex expression showing \log sub 10 6 + \log sub 10 2$

d $A LaTex expression showing \log sub 6 6 + \log sub 6 13$

e $A LaTex expression showing \log sub 6 10 + \log sub 6 2$

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

$A LaTex expression showing \log sub 9 15$

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

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

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

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

$A LaTex expression showing \log sub 7 32$

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

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

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

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

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

$A LaTex expression showing \log sub 10 42$

a $A LaTex expression showing \log sub 6 7 + \log sub 6 10$

b $A LaTex expression showing \log sub 10 10 + \log sub 10 11$

c $A LaTex expression showing \log sub 10 7 + \log sub 10 6$

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

e $A LaTex expression showing \log sub 7 10 + \log sub 7 6$