Logarithm Algebra (Product Property) - To Answer (Coefficient 1)

Level 1

This math topic focuses on applying the product property of logarithms to simplify expressions into quadratic forms and solve for variables. Each problem involves using the logarithmic product rule to merge two logarithmic expressions into a single logarithm and then formulating a quadratic equation to solve for specific variables like 'y', 'z', 't', 'x', and 'w'. Multiple choice answers are provided for each question, requiring students to determine the correct variable value that satisfies the quadratic equation derived from the initial logarithmic equality.

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

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Logarithm Algebra (Product Property) - To Answer (Coefficient 1) Worksheet

Logarithm Algebra (Product Property) - To Answer (Coefficient 1)

Use the product rule to simplify this to a quadratic and solve for 'y'

$A LaTex expression showing \log sub 9 (y + 6) + \log sub 9 (y + 3) = \log sub 9 (4)$

Use the product rule to simplify this to a quadratic and solve for 'z'

$A LaTex expression showing \log sub 9 (z - 5) + \log sub 9 (z - 8) = \log sub 9 (4)$

$A LaTex expression showing \log sub 9 (t - 2) + \log sub 9 (t + 6) = \log sub 9 (9)$

Use the product rule to simplify this to a quadratic and solve for 't'

$A LaTex expression showing \log sub 6 (z - 3) + \log sub 6 (z - 8) = \log sub 6 (6)$

Use the product rule to simplify this to a quadratic and solve for 'z'

$A LaTex expression showing \log sub 9 (y - 7) + \log sub 9 (y - 1) = \log sub 9 (7)$

Use the product rule to simplify this to a quadratic and solve for 'y'

$A LaTex expression showing \log sub 8 (x - 7) + \log sub 8 (x - 7) = \log sub 8 (1)$

Use the product rule to simplify this to a quadratic and solve for 'x'

$A LaTex expression showing \log sub 6 (w + 8) + \log sub 6 (w + 7) = \log sub 6 (6)$

Use the product rule to simplify this to a quadratic and solve for 'w'

$A LaTex expression showing \log sub 8 (m + 9) + \log sub 8 (m + 9) = \log sub 8 (1)$

Use the product rule to simplify this to a quadratic and solve for 'm'