Logarithms

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

This math topic focuses on practicing the logarithmic quotient property, which involves converting a logarithm of a quotient into a difference of logarithms. It combines the foundational concept of logarithms with operations involving decimal numbers and their expression through logarithmic functions. The problems require the transformation of a single logarithmic expression into its equivalent form by expressing division as the difference of two logarithms. Each question offers multiple choices, each showing a different way to apply the quotient property to logarithmic expressions with various bases.

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

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Logarithms - Quotient Property - Division as Decimal To Difference Worksheet

Logarithms - Quotient Property - Division as Decimal To Difference

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

$A LaTex expression showing \log sub 2 1.2$

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

b $A LaTex expression showing \log sub 6 2 - \log sub 6 5$

c $A LaTex expression showing \log sub 2 6 - \log sub 2 5$

d $A LaTex expression showing \log sub 1 6 - \log sub 1 5$

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

$A LaTex expression showing \log sub 10 0.57$

a $A LaTex expression showing \log sub 10 4 - \log sub 10 7$

b $A LaTex expression showing \log sub 10 7 - \log sub 10 4$

c $A LaTex expression showing \log sub 12 4 - \log sub 12 7$

d $A LaTex expression showing \log sub 4 10 - \log sub 4 7$

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

$A LaTex expression showing \log sub 10 4.5$

a $A LaTex expression showing \log sub 10 9 - \log sub 10 2$

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

c $A LaTex expression showing \log sub 9 2 - \log sub 9 10$

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

$A LaTex expression showing \log sub 3 1.6$

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

b $A LaTex expression showing \log sub 3 8 - \log sub 3 5$

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

d $A LaTex expression showing \log sub 5 8 - \log sub 5 5$

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

$A LaTex expression showing \log sub 10 1.6$

a $A LaTex expression showing \log sub 10 8 - \log sub 10 5$

b $A LaTex expression showing \log sub 10 5 - \log sub 10 8$

c $A LaTex expression showing \log sub 11 8 - \log sub 11 5$

d $A LaTex expression showing \log sub 8 8 - \log sub 8 5$

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

$A LaTex expression showing \log sub 9 5$

a $A LaTex expression showing \log sub 8 10 - \log sub 8 2$

b $A LaTex expression showing \log sub 9 10 - \log sub 9 2$

c $A LaTex expression showing \log sub 10 2 - \log sub 10 9$

d $A LaTex expression showing \log sub 9 2 - \log sub 9 10$

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

$A LaTex expression showing \log sub 10 1.33$

a $A LaTex expression showing \log sub 10 4 - \log sub 10 3$

b $A LaTex expression showing \log sub 11 4 - \log sub 11 3$

c $A LaTex expression showing \log sub 4 3 - \log sub 4 10$

d $A LaTex expression showing \log sub 10 3 - \log sub 10 4$

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

$A LaTex expression showing \log sub 9 0.63$

a $A LaTex expression showing \log sub 9 5 - \log sub 9 8$

b $A LaTex expression showing \log sub 8 5 - \log sub 8 8$

c $A LaTex expression showing \log sub 11 5 - \log sub 11 8$

d $A LaTex expression showing \log sub 5 9 - \log sub 5 8$

e $A LaTex expression showing \log sub 10 5 - \log sub 10 8$