Logarithms

Quotient Property - Difference to Division as Fraction (Integers) (Level 1)

This math topic focuses on utilizing the quotient property of logarithms to convert expressions involving a difference of two logarithms into a single logarithm with a fractional argument. The problems require transforming logarithmic expressions like \(\log_b a - \log_b c\) into \(\log_b \left(\frac{a}{c}\right)\), using base integers. Each problem presents the initial logarithmic expression and multiple choice answers for the equivalent single logarithmic form, honing skills in logarithmic manipulation within the introductory concepts of logarithm functions.

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 Fraction (Integers) Worksheet

Logarithms - Quotient Property - Difference to Division as Fraction (...

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

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

a $A LaTex expression showing \log sub 8 2 over 5$

b $A LaTex expression showing \log sub 5 8 over 2$

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

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

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

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

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

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

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

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

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

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

$A LaTex expression showing \log sub 4 2 - \log sub 4 7$

a $A LaTex expression showing \log sub 7 4 over 2$

b $A LaTex expression showing \log sub 4 7 over 2$

c $A LaTex expression showing \log sub 4 2 over 7$

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

$A LaTex expression showing \log sub 7 9 - \log sub 7 8$

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

b $A LaTex expression showing \log sub 7 9 over 8$

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

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

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

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

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

c $A LaTex expression showing \log sub 10 7 over 4$

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

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

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

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

c $A LaTex expression showing \log sub 3 8 over 5$

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

$A LaTex expression showing \log sub 4 6 - \log sub 4 7$

a $A LaTex expression showing \log sub 7 4 over 6$

b $A LaTex expression showing \log sub 4 7 over 6$

c $A LaTex expression showing \log sub 4 6 over 7$