Logarithm Algebra (Product Property) - To Quadratic (Coefficient N)

Level 1

This math topic covers the application of the product property of logarithms to form and simplify quadratic equations. It helps students enhance their skills by converting logarithmic equations into quadratic forms using variables such as 'w', 'q', 't', and 'y'. Each problem is presented with multiple-choice answers showcasing different quadratic equations derived from applying the logarithmic product rule. This advanced exercise is designed to improve students' understanding of logarithmic functions within the broader scope of algebra.

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

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Logarithm Algebra (Product Property) - To Quadratic (Coefficient N) Worksheet

Logarithm Algebra (Product Property) - To Quadratic (Coefficient N)

$A LaTex expression showing \log sub 7 (-2w + 3) + \log sub 7 (2w + 5) = \log sub 7 (7)$

Use the product rule to simplify this to a quadratic of variable 'w'

A LaTex expression showing -4w to the power of 2 - 4w + 8 = 0

A LaTex expression showing -3w to the power of 2 - 3w + 10 = 0

A LaTex expression showing -3w to the power of 2 - 4w + 7 = 0

$A LaTex expression showing \log sub 10 (5q + 8) + \log sub 10 (5q + 7) = \log sub 10 (6)$

Use the product rule to simplify this to a quadratic of variable 'q'

A LaTex expression showing 25q to the power of 2 + 75q + 50 = 0

A LaTex expression showing 25q to the power of 2 + 75q + 48 = 0

A LaTex expression showing 25q to the power of 2 + 76q + 53 = 0

$A LaTex expression showing \log sub 3 (4q + 3) + \log sub 3 (-4q + 3) = \log sub 3 (9)$

Use the product rule to simplify this to a quadratic of variable 'q'

A LaTex expression showing -16q to the power of 2 + 0q + 0 = 0

A LaTex expression showing -16q to the power of 2 + 2q + 3 = 0

A LaTex expression showing -17q to the power of 2 + 0q - 3 = 0

$A LaTex expression showing \log sub 4 (-3t - 5) + \log sub 4 (-6t - 8) = \log sub 4 (4)$

Use the product rule to simplify this to a quadratic of variable 't'

A LaTex expression showing 17t to the power of 2 + 52t + 40 = 0

A LaTex expression showing 18t to the power of 2 + 54t + 36 = 0

A LaTex expression showing 19t to the power of 2 + 56t + 33 = 0

$A LaTex expression showing \log sub 2 (-1y - 3) + \log sub 2 (y + 9) = \log sub 2 (8)$

Use the product rule to simplify this to a quadratic of variable 'y'

A LaTex expression showing -1y to the power of 2 - 12y - 35 = 0

A LaTex expression showing -1y to the power of 2 - 14y - 34 = 0

A LaTex expression showing -2y to the power of 2 - 13y - 35 = 0

$A LaTex expression showing \log sub 10 (4w - 8) + \log sub 10 (w - 1) = \log sub 10 (8)$

Use the product rule to simplify this to a quadratic of variable 'w'

A LaTex expression showing 4w to the power of 2 - 12w + 3 = 0

A LaTex expression showing 3w to the power of 2 - 11w + 3 = 0

A LaTex expression showing 4w to the power of 2 - 12w + 0 = 0

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

Use the product rule to simplify this to a quadratic of variable 'y'

A LaTex expression showing -9y to the power of 2 - 31y - 35 = 0

A LaTex expression showing -7y to the power of 2 - 31y - 31 = 0

A LaTex expression showing -8y to the power of 2 - 32y - 32 = 0

$A LaTex expression showing \log sub 10 (2t - 4) + \log sub 10 (t + 1) = \log sub 10 (8)$

Use the product rule to simplify this to a quadratic of variable 't'

A LaTex expression showing 2t to the power of 2 - 2t - 12 = 0

A LaTex expression showing 2t to the power of 2 - 4t - 11 = 0

A LaTex expression showing 3t to the power of 2 - 2t - 14 = 0