Logarithm Algebra (Power Property) - Isolote Exponent, One Binomial (Coefficient N) to Partial Answer

Level 1

This math topic focuses on applying the power property of logarithms to isolate exponents in equations involving binomials. Students solve problems where they simplify equations through logarithms, transforming exponential forms into logarithmic forms. Each question presents a scenario where an equation of powers with vague binomial exponents on both sides needs conversion using logarithms. The worksheet offers multiple-choice answers for each query, testing a student’s ability to utilize the logarithm function's power property effectively within advanced logarithmic functions.

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

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Logarithm Algebra (Power Property) - Isolote Exponent, One Binomial (Coefficient N) to Partial Answer Worksheet

Logarithm Algebra (Power Property) - Isolote Exponent, One Binomial (...

Use the power rule to simplify this equation

A LaTex expression showing 4 to the power of (-1z + 3) = 3 to the power of (-7z )

a $A LaTex expression showing (-1z + 3)\ln{4} = (-7z )\ln{3}$

b $A LaTex expression showing (-1z - 3)\ln{4} = (-7z - 2)\ln{3}$

c $A LaTex expression showing (3z - 1)\ln{4} = (2z - 7)\ln{3}$

Use the power rule to simplify this equation

A LaTex expression showing 3 to the power of (7x - 5) = 7 to the power of (-4x )

a $A LaTex expression showing (7x - 5)\ln{3} = (-4x )\ln{7}$

b $A LaTex expression showing (7x + 5)\ln{3} = (-4x - 2)\ln{7}$

c $A LaTex expression showing (-5x + 7)\ln{3} = (2x - 4)\ln{7}$

Use the power rule to simplify this equation

A LaTex expression showing 5 to the power of (5n + 4) = 10 to the power of (-3n )

a $A LaTex expression showing (4n + 5)\ln{5} = (2n - 3)\ln{10}$

b $A LaTex expression showing (5n - 4)\ln{5} = (-3n - 2)\ln{10}$

c $A LaTex expression showing (5n + 4)\ln{5} = (-3n )\ln{10}$

Use the power rule to simplify this equation

A LaTex expression showing 10 to the power of (-5n + 3) = 7 to the power of (-5n )

a $A LaTex expression showing (3n - 5)\ln{10} = (2n - 5)\ln{7}$

b $A LaTex expression showing (-5n + 3)\ln{10} = (-5n )\ln{7}$

c $A LaTex expression showing (-5n - 3)\ln{10} = (-5n - 2)\ln{7}$

Use the power rule to simplify this equation

A LaTex expression showing 4 to the power of (-1z - 5) = 7 to the power of (-7z )

a $A LaTex expression showing (-5z - 1)\ln{4} = (2z - 7)\ln{7}$

b $A LaTex expression showing (-1z - 5)\ln{4} = (-7z )\ln{7}$

c $A LaTex expression showing (-1z + 5)\ln{4} = (-7z - 2)\ln{7}$

Use the power rule to simplify this equation

A LaTex expression showing 8 to the power of (-8q - 2) = 9 to the power of (-7q )

a $A LaTex expression showing (-8q + 2)\ln{8} = (-7q - 2)\ln{9}$

b $A LaTex expression showing (-8q - 2)\ln{8} = (-7q )\ln{9}$

c $A LaTex expression showing (-2q - 8)\ln{8} = (2q - 7)\ln{9}$

Use the power rule to simplify this equation

A LaTex expression showing 6 to the power of (5p - 3) = 7 to the power of (3p )

a $A LaTex expression showing (5p + 3)\ln{6} = (3p - 2)\ln{7}$

b $A LaTex expression showing (-3p + 5)\ln{6} = (2p + 3)\ln{7}$

c $A LaTex expression showing (5p - 3)\ln{6} = (3p )\ln{7}$

Use the power rule to simplify this equation

A LaTex expression showing 3 to the power of (-7y - 6) = 8 to the power of (5y )

a $A LaTex expression showing (-7y + 6)\ln{3} = (5y - 2)\ln{8}$

b $A LaTex expression showing (-7y - 6)\ln{3} = (5y )\ln{8}$

c $A LaTex expression showing (-6y - 7)\ln{3} = (2y + 5)\ln{8}$