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

Level 1

This math topic focuses on the application of logarithmic functions, specifically employing the quotient property to solve algebraic expressions. It involves simplifying the given logarithmic expressions to quadratic equations and determining the values of variables (labeled as 'r', 't', 'z', and 'q'). Each problem is structured to test understanding and manipulation of logarithms with different bases and is aimed at providing practice in solving for variables under advanced logarithm functions. There are a variety of expressions presented that cover various algebraic forms demanding skills in both logarithms and quadratic equations.

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

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Logarithm Algebra (Quotient Property) - To Answer (Coefficient N) Worksheet

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

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

Use the quotient rule to simplify this to a quadratic and solve for 'r'

$A LaTex expression showing \log sub 2 (7r - 5) - \log sub 2 (-1r + 11) = \log sub 2 (1r)$

Use the quotient rule to simplify this to a quadratic and solve for 'r'

$A LaTex expression showing \log sub 8 (9t + 9) - \log sub 8 (t + 5) = \log sub 8 (3t)$

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

$A LaTex expression showing \log sub 4 (-11z + 2) - \log sub 4 (-2z + 11) = \log sub 4 (-1z)$

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

$A LaTex expression showing \log sub 2 (7q - 4) - \log sub 2 (-1q + 7) = \log sub 2 (1q)$

Use the quotient rule to simplify this to a quadratic and solve for 'q'

$A LaTex expression showing \log sub 9 (-1q + 6) - \log sub 9 (q - 2) = \log sub 9 (1q)$

Use the quotient rule to simplify this to a quadratic and solve for 'q'

$A LaTex expression showing \log sub 2 (-1r + 8) - \log sub 2 (-4r + 5) = \log sub 2 (-1r)$

Use the quotient rule to simplify this to a quadratic and solve for 'r'

$A LaTex expression showing \log sub 7 (-4m + 8) - \log sub 7 (8m - 4) = \log sub 7 (1m)$

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