Logarithms

Quotient Property - Division as Fraction To Difference (Variables) (Level 1)

This math topic focuses on applying the quotient property of logarithms to convert a logarithm of a quotient into a difference of logarithms. Each problem involves variables and asks students to rewrite a logarithmic expression of the form \(\log_b{\frac{m}{n}}\) into the form \(\log_b m - \log_b n\) or vice versa, with different variable and base combinations, offering practice on converting fractional logarithmic expressions and reinforcing the understanding of the quotient rule in logarithms.

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

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Logarithms - Quotient Property - Division as Fraction To Difference (Variables) Worksheet

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

$A LaTex expression showing \log sub p m over r$

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

a $A LaTex expression showing \log sub p m - \log sub p r$

b $A LaTex expression showing \log sub p r - \log sub p m$

$A LaTex expression showing \log sub p y over n$

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

a $A LaTex expression showing \log sub p n - \log sub p y$

b $A LaTex expression showing \log sub p y - \log sub p n$

$A LaTex expression showing \log sub p q over w$

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

a $A LaTex expression showing \log sub p q - \log sub p w$

b $A LaTex expression showing \log sub p w - \log sub p q$

$A LaTex expression showing \log sub t z over m$

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

a $A LaTex expression showing \log sub t m - \log sub t z$

b $A LaTex expression showing \log sub t z - \log sub t m$

$A LaTex expression showing \log sub z p over w$

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

a $A LaTex expression showing \log sub z w - \log sub z p$

b $A LaTex expression showing \log sub z p - \log sub z w$

$A LaTex expression showing \log sub p n over x$

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

a $A LaTex expression showing \log sub p n - \log sub p x$

b $A LaTex expression showing \log sub p x - \log sub p n$

$A LaTex expression showing \log sub m y over q$

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

a $A LaTex expression showing \log sub m q - \log sub m y$

b $A LaTex expression showing \log sub m y - \log sub m q$

$A LaTex expression showing \log sub p n over m$

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

a $A LaTex expression showing \log sub p m - \log sub p n$

b $A LaTex expression showing \log sub p n - \log sub p m$