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

Level 1

This math topic focuses on applying the quotient property of logarithms to simplify logarithmic expressions and then converting these into quadratic equations. It combines advanced knowledge of logarithm functions with algebraic manipulation to create quadratic equations. The problems given require the learner to use the quotient rule in logarithms to form a quadratic equation in one variable (like 'w', 'z', 'n', 'm', 'r', 'p'), and then select the correct quadratic equation from multiple choices. Each question features a different logarithmic expression with the same fundamental skill application.

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 N) Worksheet

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

$A LaTex expression showing \log sub 4 (9w + 4) - \log sub 4 (w + 6) = \log sub 4 (1w)$

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

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

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

A LaTex expression showing -1w to the power of 2 + 3w + 4 = 0

$A LaTex expression showing \log sub 3 (-8z + 10) - \log sub 3 (z + 1) = \log sub 3 (1z)$

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

A LaTex expression showing 0z to the power of 2 - 7z + 12 = 0

A LaTex expression showing -2z to the power of 2 - 9z + 11 = 0

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

$A LaTex expression showing \log sub 9 (-6n + 10) - \log sub 9 (10n - 6) = \log sub 9 (1n)$

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

A LaTex expression showing -11n to the power of 2 + 1n + 7 = 0

A LaTex expression showing -10n to the power of 2 + 2n + 7 = 0

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

$A LaTex expression showing \log sub 7 (-5m - 1) - \log sub 7 (m + 5) = \log sub 7 (-1m)$

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

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

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

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

$A LaTex expression showing \log sub 4 (-3r + 9) - \log sub 4 (r + 5) = \log sub 4 (1r)$

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

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

A LaTex expression showing 0r to the power of 2 - 7r + 13 = 0

A LaTex expression showing -1r to the power of 2 - 10r + 12 = 0

$A LaTex expression showing \log sub 6 (10w - 4) - \log sub 6 (-2w + 5) = \log sub 6 (2w)$

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

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

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

A LaTex expression showing 5w to the power of 2 - 2w - 3 = 0

$A LaTex expression showing \log sub 2 (3p + 4) - \log sub 2 (-2p - 1) = \log sub 2 (-1p)$

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

A LaTex expression showing -2p to the power of 2 + 0p + 7 = 0

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

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

$A LaTex expression showing \log sub 2 (2x + 5) - \log sub 2 (x + 4) = \log sub 2 (-1x)$

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

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

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

A LaTex expression showing x to the power of 2 + 5x + 8 = 0