Logarithms

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

This math topic involves practicing the application of the product property of logarithms to rewrite sums of logarithms as a single logarithm. Each problem presents expressions where two logarithms with the same base are added, and students are asked to use the product property to convert these sums into a product under a single log. The problems include different variables and bases, ensuring familiarity with employing the product property across various expressions. The focus is on reinforcing understanding of logarithmic identities in an introductory context 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 - Sum to Product (Variables) Worksheet

Logarithms - Product Property - Sum to Product (Variables)

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

$A LaTex expression showing \log sub m x + \log sub m p$

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

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

c $A LaTex expression showing \log sub m x over p$

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

$A LaTex expression showing \log sub y w + \log sub y p$

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

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

c $A LaTex expression showing \log sub y w over p$

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

$A LaTex expression showing \log sub z r + \log sub z w$

a $A LaTex expression showing \log sub w (z times r)$

b $A LaTex expression showing \log sub z (r times w)$

c $A LaTex expression showing \log sub z r over w$

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

$A LaTex expression showing \log sub m w + \log sub m x$

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

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

c $A LaTex expression showing \log sub m w over x$

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

$A LaTex expression showing \log sub q r + \log sub q p$

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

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

c $A LaTex expression showing \log sub q r over p$

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

$A LaTex expression showing \log sub p t + \log sub p y$

a $A LaTex expression showing \log sub y (p times t)$

b $A LaTex expression showing \log sub p (t times y)$

c $A LaTex expression showing \log sub p t over y$

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

$A LaTex expression showing \log sub m t + \log sub m r$

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

b $A LaTex expression showing \log sub m t over r$

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

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

$A LaTex expression showing \log sub r x + \log sub r z$

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

b $A LaTex expression showing \log sub r x over z$

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