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

Level 1

This math topic explores advanced applications of logarithmic functions, specifically focusing on the power rule within logarithmic algebra leading to quadratic equations. Problems require simplifying logarithmic equations featuring a variable (like y, w, p, m, x) by applying the power property of logarithms. Each question presents a logarithmic equation and demands conversion into an equivalent quadratic or linear form to isolate and solve for the variable. Multiple-choice answers illustrate different outcomes of applying the power rule correctly or incorrectly in solving the equations.

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

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Logarithm Algebra (Power Property) - To Quadratic (Coefficient N) Worksheet

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Logarithm Algebra (Power Property) - To Quadratic (Coefficient N)
1
Use the power rule to simplify this to an equation with variable 'y'
A LaTex expression showing 2\log sub 7 (y + 3) = \log sub 7 (9)
a A LaTex expression showing 2(y + 3) = 81
b A LaTex expression showing (y + 6) = 81
c A LaTex expression showing (y + 3) to the power of 2 = 81
2
Use the power rule to simplify this to an equation with variable 'w'
A LaTex expression showing 2\log sub 6 (w - 2) = \log sub 6 (1)
a A LaTex expression showing (w - 4) = 1
b A LaTex expression showing (w - 2) to the power of 2 = 1
c A LaTex expression showing 2(w - 2) = 1
3
Use the power rule to simplify this to an equation with variable 'p'
A LaTex expression showing 2\log sub 3 (p - 6) = \log sub 3 (9)
a A LaTex expression showing (p - 12) = 81
b A LaTex expression showing (p - 6) to the power of 2 = 81
c A LaTex expression showing 2(p - 6) = 81
4
Use the power rule to simplify this to an equation with variable 'm'
A LaTex expression showing 2\log sub 6 (3m + 9) = \log sub 6 (9)
a A LaTex expression showing 2(3m + 9) = 81
b A LaTex expression showing (3m + 18) = 81
c A LaTex expression showing (3m + 9) to the power of 2 = 81
5
Use the power rule to simplify this to an equation with variable 'x'
A LaTex expression showing 2\log sub 5 (-3x + 9) = \log sub 5 (9)
a A LaTex expression showing (-3x + 9) to the power of 2 = 81
b A LaTex expression showing 2(-3x + 9) = 81
c A LaTex expression showing (-3x + 18) = 81
6
Use the power rule to simplify this to an equation with variable 'w'
A LaTex expression showing 3\log sub 2 (-1w + 2) = \log sub 2 (4)
a A LaTex expression showing 3(-1w + 2) = 64
b A LaTex expression showing (-1w + 6) = 64
c A LaTex expression showing (-1w + 2) to the power of 3 = 64
7
Use the power rule to simplify this to an equation with variable 'p'
A LaTex expression showing 3\log sub 2 (2p + 4) = \log sub 2 (4)
a A LaTex expression showing (2p + 12) = 64
b A LaTex expression showing (2p + 4) to the power of 3 = 64
c A LaTex expression showing 3(2p + 4) = 64
8
Use the power rule to simplify this to an equation with variable 'p'
A LaTex expression showing 2\log sub 8 (p - 3) = \log sub 8 (4)
a A LaTex expression showing 2(p - 3) = 16
b A LaTex expression showing (p - 6) = 16
c A LaTex expression showing (p - 3) to the power of 2 = 16