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

Level 1

This topic focuses on utilizing the quotient rule of logarithms for simplifying expressions into quadratic equations and then solving for the variable. It is designed for advanced students studying logarithm functions, specifically emphasizing algebraic manipulation and problem-solving skills involving logarithmic equations. The exercises require combining like terms and applying algebraic techniques to find values of variables such as 'w', 'm', 'q', 'x', and 'z' through simplified logarithmic expressions depicted in the problems. Each problem provides multiple choice answers.

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

Worksheet ViewUnit

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

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

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

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

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

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

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

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

$A LaTex expression showing \log sub 7 (w + 3) - \log sub 7 (w + 3) = \log sub 7 (1w)$

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

$A LaTex expression showing \log sub 7 (x + 3) - \log sub 7 (x + 3) = \log sub 7 (1x)$

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

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

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

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

$A LaTex expression showing \log sub 3 (x + 7) - \log sub 3 (x + 7) = \log sub 3 (1x)$

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

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