Logarithms

Product Property - Product to Sum (Variables) (Level 1)

This topic focuses on practicing the product property of logarithms to convert the logarithm of a product into a sum of logarithms involving variables. The problems require converting expressions like \(\log_x(pw)\) into forms such as \(\log_x p + \log_x w\), in line with the logarithmic identity \(\log_b(xy) = \log_b x + \log_b y\). Each question gives a logarithmic expression involving a multiplication inside the log function, and students must select the correct transformed expression based on the product property. This forms part of an introductory unit on logarithmic functions.

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

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Logarithms - Product Property - Product to Sum (Variables) Worksheet

Logarithms - Product Property - Product to Sum (Variables)

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

$A LaTex expression showing \log sub x (p times w)$

a $A LaTex expression showing p times \log sub x w$

b $A LaTex expression showing \log sub x p + \log sub x w$

c $A LaTex expression showing \log sub w x + \log sub x p$

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

$A LaTex expression showing \log sub p (n times m)$

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

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

c $A LaTex expression showing \log sub p n + \log sub p m$

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

$A LaTex expression showing \log sub m (p times n)$

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

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

c $A LaTex expression showing \log sub m p + \log sub m n$

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

$A LaTex expression showing \log sub m (p times q)$

a $A LaTex expression showing p times \log sub m q$

b $A LaTex expression showing \log sub m p + \log sub m q$

c $A LaTex expression showing \log sub q m + \log sub m p$

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

$A LaTex expression showing \log sub x (y times z)$

a $A LaTex expression showing \log sub x y + \log sub x z$

b $A LaTex expression showing y times \log sub x z$

c $A LaTex expression showing \log sub z x + \log sub x y$

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

$A LaTex expression showing \log sub x (q times z)$

a $A LaTex expression showing \log sub x q + \log sub x z$

b $A LaTex expression showing q times \log sub x z$

c $A LaTex expression showing \log sub z x + \log sub x q$

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

$A LaTex expression showing \log sub z (m times t)$

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

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

c $A LaTex expression showing \log sub t z + \log sub z m$

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

$A LaTex expression showing \log sub r (y times n)$

a $A LaTex expression showing \log sub r y + \log sub r n$

b $A LaTex expression showing \log sub n r + \log sub r y$

c $A LaTex expression showing y times \log sub r n$