Logarithm Algebra (Quotient Property) - To Quadratic (Coefficient 1)

Level 1

This math topic focuses on advanced logarithm functions, specifically using the quotient property to simplify logarithmic expressions to quadratic equations with a coefficient of 1. It involves manipulating various logarithmic expressions, each subtracting two logarithms with the same base, and simplifying the resultant expressions into forms of quadratic equations. Each problem offers multiple choices for the simplified quadratic expression, indicating an emphasis on understanding and applying the quotient rule effectively in the context of algebraic transformation.

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

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Logarithm Algebra (Quotient Property) - To Quadratic (Coefficient 1) Worksheet

Logarithm Algebra (Quotient Property) - To Quadratic (Coefficient 1)

$A LaTex expression showing \log sub 7 (p + 4) - \log sub 7 (p + 1) = \log sub 7 (1p)$

Use the quotient rule to simplify this to a quadratic of variable 'p'

A LaTex expression showing -1p to the power of 2 + 0p + 4 = 0

A LaTex expression showing -1p to the power of 2 + 1p + 2 = 0

A LaTex expression showing 0p to the power of 2 + 2p + 2 = 0

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

Use the quotient rule to simplify this to a quadratic of variable 'n'

A LaTex expression showing -1n to the power of 2 - 9n + 13 = 0

A LaTex expression showing -1n to the power of 2 - 7n + 8 = 0

A LaTex expression showing -1n to the power of 2 - 8n + 9 = 0

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

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

A LaTex expression showing -1y to the power of 2 - 3y + 7 = 0

A LaTex expression showing -2y to the power of 2 - 5y + 14 = 0

A LaTex expression showing -1y to the power of 2 - 3y + 10 = 0

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

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

A LaTex expression showing t to the power of 2 + 5t + 6 = 0

A LaTex expression showing t to the power of 2 + 4t + 3 = 0

A LaTex expression showing 0t to the power of 2 + 2t + 6 = 0

$A LaTex expression showing \log sub 3 (t + 10) - \log sub 3 (t + 10) = \log sub 3 (1t)$

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

A LaTex expression showing -1t to the power of 2 - 8t + 10 = 0

A LaTex expression showing -1t to the power of 2 - 10t + 13 = 0

A LaTex expression showing -1t to the power of 2 - 9t + 10 = 0

$A LaTex expression showing \log sub 7 (y + 6) - \log sub 7 (y + 4) = \log sub 7 (-1y)$

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

A LaTex expression showing 2y to the power of 2 + 6y + 5 = 0

A LaTex expression showing y to the power of 2 + 5y + 6 = 0

A LaTex expression showing 0y to the power of 2 + 3y + 9 = 0

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

Use the quotient rule to simplify this to a quadratic of variable 'z'

A LaTex expression showing z to the power of 2 + 9z + 8 = 0

A LaTex expression showing 0z to the power of 2 + 7z + 11 = 0

A LaTex expression showing 0z to the power of 2 + 10z + 6 = 0

$A LaTex expression showing \log sub 2 (x + 5) - \log sub 2 (x + 5) = \log sub 2 (1x)$

Use the quotient rule to simplify this to a quadratic of variable 'x'

A LaTex expression showing -1x to the power of 2 - 3x + 8 = 0

A LaTex expression showing -1x to the power of 2 - 4x + 5 = 0

A LaTex expression showing -1x to the power of 2 - 4x + 6 = 0