Logarithms

Quotient Property - Difference to Division as Decimal (Level 1)

This math topic focuses on the quotient property of logarithms, teaching students how to convert the difference of two logarithms to a single logarithm involving division expressed as a decimal. The problems presented ask students to apply the quotient property (i.e., \(\log_b a - \log_b c = \log_b (a/c)\)) to various base logarithmic expressions. Each question provides a different set of logarithmic expressions and the task is to simplify these expressions by converting the difference to a division. The format is multiple-choice, allowing students to select the correctly simplified logarithmic expression based on the applied quotient property.

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

more

Worksheet ViewUnit

Logarithms - Quotient Property - Difference to Division as Decimal Worksheet

Logarithms - Quotient Property - Difference to Division as Decimal

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

$A LaTex expression showing \log sub 6 10 - \log sub 6 9$

a $A LaTex expression showing \log sub 6 1.11$

b $A LaTex expression showing \log sub 1.11 6$

c $A LaTex expression showing \log sub 7 1.11$

d $A LaTex expression showing \log sub 6 3.11$

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

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

a $A LaTex expression showing \log sub 1.67 9$

b $A LaTex expression showing \log sub 9 1.67$

c $A LaTex expression showing \log sub 9 -0.33$

d $A LaTex expression showing \log sub 9 3.67$

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

$A LaTex expression showing \log sub 6 7 - \log sub 6 8$

a $A LaTex expression showing \log sub 5 0.88$

b $A LaTex expression showing \log sub 6 -1.13$

c $A LaTex expression showing \log sub 4 0.88$

d $A LaTex expression showing \log sub 6 0.88$

e $A LaTex expression showing \log sub 0.88 6$

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

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

a $A LaTex expression showing \log sub 6 -1.78$

b $A LaTex expression showing \log sub 6 2.22$

c $A LaTex expression showing \log sub 6 0.22$

d $A LaTex expression showing \log sub 6 1.22$

e $A LaTex expression showing \log sub 6 -0.78$

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

$A LaTex expression showing \log sub 9 7 - \log sub 9 10$

a $A LaTex expression showing \log sub 9 -0.3$

b $A LaTex expression showing \log sub 9 -1.3$

c $A LaTex expression showing \log sub 0.7 9$

d $A LaTex expression showing \log sub 9 0.7$

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

$A LaTex expression showing \log sub 5 9 - \log sub 5 7$

a $A LaTex expression showing \log sub 5 1.29$

b $A LaTex expression showing \log sub 5 3.29$

c $A LaTex expression showing \log sub 1.29 5$

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

$A LaTex expression showing \log sub 8 7 - \log sub 8 4$

a $A LaTex expression showing \log sub 8 3.75$

b $A LaTex expression showing \log sub 6 1.75$

c $A LaTex expression showing \log sub 8 1.75$

d $A LaTex expression showing \log sub 1.75 8$

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

$A LaTex expression showing \log sub 5 6 - \log sub 5 7$

a $A LaTex expression showing \log sub 5 -0.14$

b $A LaTex expression showing \log sub 5 0.86$

c $A LaTex expression showing \log sub 7 0.86$

d $A LaTex expression showing \log sub 3 0.86$