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

Level 1

This math topic focuses on the application of the logarithmic product property to solve algebraic equations. Each problem requires combining logarithmic terms to form a quadratic equation, which is then solved to find the variable. The topic is part of an advanced logarithm functions unit, likely aimed at reinforcing skills in manipulating and solving logarithmic expressions.

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

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

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

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

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

A LaTex expression showing x=-9

A LaTex expression showing x=-2

A LaTex expression showing x=0

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

Use the product rule to simplify this to a quadratic and solve for 'n'

A LaTex expression showing n=-8

A LaTex expression showing n=9

A LaTex expression showing n=0

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

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

A LaTex expression showing z=-2

A LaTex expression showing z=5

A LaTex expression showing z=6

$A LaTex expression showing \log sub 9 (-1r - 3) + \log sub 9 (-1r - 8) = \log sub 9 (6)$

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

A LaTex expression showing r=-9

A LaTex expression showing r=-19

A LaTex expression showing r=-1

$A LaTex expression showing \log sub 10 (-2x - 8) + \log sub 10 (-1x - 3) = \log sub 10 (4)$

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

A LaTex expression showing x=3

A LaTex expression showing x=-5

A LaTex expression showing x=-7

$A LaTex expression showing \log sub 3 (x - 7) + \log sub 3 (x - 3) = \log sub 3 (5)$

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

A LaTex expression showing x=17

A LaTex expression showing x=8

A LaTex expression showing x=14

$A LaTex expression showing \log sub 7 (2w + 9) + \log sub 7 (-2w - 1) = \log sub 7 (7)$

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

a $A LaTex expression showing w=-4\\w=-1$

b $A LaTex expression showing w=-14\\w=8$

c $A LaTex expression showing w=-12\\w=7$

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

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

A LaTex expression showing m=1

A LaTex expression showing m=-3