Logarithm Algebra (Power Property) - Isolote Exponent, Two Binomials (Coefficient N) to Partial Answer

Level 1

This math topic focuses on applying the power property of logarithms to solve equations where exponents need to be manipulated and isolated. These problems involve equating two expressions of different bases by simplifying and comparing the logarithmic forms. Each question presents an equation where students must use logarithms to isolate and compare coefficients effectively. The exercises are designed as typical format problems with multiple-choice answers, providing students with practice in using logarithms to handle equations involving powers, which are a critical component of advanced logarithmic functions.

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

Logarithm Algebra (Power Property) - Isolote Exponent, Two Binomials ...

Use the power rule to simplify this equation

A LaTex expression showing 2 to the power of (-4r - 8) = 8 to the power of (6r - 8)

a $A LaTex expression showing (-4r - 8)\ln{2} = (6r - 8)\ln{8}$

b $A LaTex expression showing (-4r + 8)\ln{2} = (6r + 8)\ln{8}$

c $A LaTex expression showing (-8r - 4)\ln{2} = (-8r + 6)\ln{8}$

Use the power rule to simplify this equation

A LaTex expression showing 9 to the power of (8y - 3) = 8 to the power of (-9y - 7)

a $A LaTex expression showing (8y - 3)\ln{9} = (-9y - 7)\ln{8}$

b $A LaTex expression showing (8y + 3)\ln{9} = (-9y + 7)\ln{8}$

c $A LaTex expression showing (-3y + 8)\ln{9} = (-7y - 9)\ln{8}$

Use the power rule to simplify this equation

A LaTex expression showing 6 to the power of (5r + 1) = 3 to the power of (-5r + 5)

a $A LaTex expression showing (5r - 1)\ln{6} = (-5r - 5)\ln{3}$

b $A LaTex expression showing (5r + 1)\ln{6} = (-5r + 5)\ln{3}$

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

Use the power rule to simplify this equation

A LaTex expression showing 7 to the power of (-9p - 6) = 4 to the power of (-6p + 1)

a $A LaTex expression showing (-9p - 6)\ln{7} = (-6p + 1)\ln{4}$

b $A LaTex expression showing (-6p - 9)\ln{7} = (p - 6)\ln{4}$

c $A LaTex expression showing (-9p + 6)\ln{7} = (-6p - 1)\ln{4}$

Use the power rule to simplify this equation

A LaTex expression showing 6 to the power of (-9y - 9) = 9 to the power of (7y + 5)

a $A LaTex expression showing (-9y - 9)\ln{6} = (7y + 5)\ln{9}$

b $A LaTex expression showing (-9y - 9)\ln{6} = (5y + 7)\ln{9}$

c $A LaTex expression showing (-9y + 9)\ln{6} = (7y - 5)\ln{9}$

Use the power rule to simplify this equation

A LaTex expression showing 8 to the power of (-7z + 6) = 10 to the power of (-9z + 5)

a $A LaTex expression showing (6z - 7)\ln{8} = (5z - 9)\ln{10}$

b $A LaTex expression showing (-7z + 6)\ln{8} = (-9z + 5)\ln{10}$

c $A LaTex expression showing (-7z - 6)\ln{8} = (-9z - 5)\ln{10}$

Use the power rule to simplify this equation

A LaTex expression showing 9 to the power of (-2t - 3) = 6 to the power of (-1t + 9)

a $A LaTex expression showing (-2t - 3)\ln{9} = (-1t + 9)\ln{6}$

b $A LaTex expression showing (-3t - 2)\ln{9} = (9t - 1)\ln{6}$

c $A LaTex expression showing (-2t + 3)\ln{9} = (-1t - 9)\ln{6}$

Use the power rule to simplify this equation

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

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

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

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