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

Level 1

This topic focuses on practicing the use of the logarithmic product property to simplify expressions into quadratic equations. These problems involve combining logarithmic terms of the same base using the product property and then equating them to another logarithm, resulting in a quadratic equation in one variable. Each question includes multiple-choice answers, giving learners the chance to solve for the coefficients and constants in the quadratic equations derived from logarithmic identities. The exercises are advanced and designed to enhance understanding of both logarithms and quadratic equations.

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

more

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

Mobius Math Academy logo
Logarithm Algebra (Product Property) - To Quadratic (Coefficient 1)
1
A LaTex expression showing \log sub 10 (n - 6) + \log sub 10 (n - 3) = \log sub 10 (4)
Use the product rule to simplify this to a quadratic of variable 'n'
a A LaTex expression showing 2n to the power of 2 - 11n + 18 = 0
b A LaTex expression showing n to the power of 2 - 9n + 14 = 0
c A LaTex expression showing n to the power of 2 - 11n + 15 = 0
2
A LaTex expression showing \log sub 6 (p - 9) + \log sub 6 (p - 8) = \log sub 6 (2)
Use the product rule to simplify this to a quadratic of variable 'p'
a A LaTex expression showing p to the power of 2 - 17p + 72 = 0
b A LaTex expression showing 0p to the power of 2 - 19p + 68 = 0
c A LaTex expression showing p to the power of 2 - 17p + 70 = 0
3
A LaTex expression showing \log sub 9 (w - 3) + \log sub 9 (w - 9) = \log sub 9 (7)
Use the product rule to simplify this to a quadratic of variable 'w'
a A LaTex expression showing w to the power of 2 - 12w + 20 = 0
b A LaTex expression showing 2w to the power of 2 - 13w + 20 = 0
c A LaTex expression showing w to the power of 2 - 12w + 24 = 0
4
A LaTex expression showing \log sub 3 (w + 1) + \log sub 3 (w - 5) = \log sub 3 (7)
Use the product rule to simplify this to a quadratic of variable 'w'
a A LaTex expression showing 0w to the power of 2 - 3w - 14 = 0
b A LaTex expression showing w to the power of 2 - 4w - 12 = 0
c A LaTex expression showing 2w to the power of 2 - 6w - 12 = 0
5
A LaTex expression showing \log sub 6 (x - 7) + \log sub 6 (x - 7) = \log sub 6 (4)
Use the product rule to simplify this to a quadratic of variable 'x'
a A LaTex expression showing x to the power of 2 - 14x + 45 = 0
b A LaTex expression showing x to the power of 2 - 14x + 48 = 0
c A LaTex expression showing 2x to the power of 2 - 14x + 47 = 0
6
A LaTex expression showing \log sub 5 (p - 8) + \log sub 5 (p - 7) = \log sub 5 (6)
Use the product rule to simplify this to a quadratic of variable 'p'
a A LaTex expression showing p to the power of 2 - 15p + 50 = 0
b A LaTex expression showing 2p to the power of 2 - 14p + 51 = 0
c A LaTex expression showing 2p to the power of 2 - 15p + 51 = 0
7
A LaTex expression showing \log sub 10 (z - 5) + \log sub 10 (z + 3) = \log sub 10 (9)
Use the product rule to simplify this to a quadratic of variable 'z'
a A LaTex expression showing z to the power of 2 - 1z - 21 = 0
b A LaTex expression showing z to the power of 2 - 2z - 24 = 0
c A LaTex expression showing 2z to the power of 2 - 4z - 27 = 0
8
A LaTex expression showing \log sub 5 (w - 2) + \log sub 5 (w - 4) = \log sub 5 (3)
Use the product rule to simplify this to a quadratic of variable 'w'
a A LaTex expression showing 2w to the power of 2 - 7w + 4 = 0
b A LaTex expression showing w to the power of 2 - 6w + 5 = 0
c A LaTex expression showing 0w to the power of 2 - 7w + 2 = 0