Logarithm Algebra (Power Property) - Isolote Exponent, One Binomial (Coefficient 1) to Partial Answer

Level 1

This math topic focuses on using the power property of logarithms to isolate variables in exponential equations. Students are presented with equations where they need to apply logarithmic transformations to simplify and solve them, with variables typically in binomial forms having coefficient 1. Multiple-choice questions guide learners to determine the correct logarithmic form of given exponential equations. This advanced topic is part of a broader unit on logarithmic functions, emphasizing algebraic manipulation of logarithms and exponents.

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Logarithm Algebra (Power Property) - Isolote Exponent, One Binomial (Coefficient 1) to Partial Answer Worksheet

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

Use the power rule to simplify this equation

A LaTex expression showing 6 to the power of (y + 3) = 4 to the power of (y )

a $A LaTex expression showing (y - 3)\ln{6} = (y - 2)\ln{4}$

b $A LaTex expression showing (y + 3)\ln{6} = (y )\ln{4}$

c $A LaTex expression showing (3y + 1)\ln{6} = (2y + 1)\ln{4}$

Use the power rule to simplify this equation

A LaTex expression showing 9 to the power of (t + 9) = 8 to the power of (t )

a $A LaTex expression showing (9t + 1)\ln{9} = (2t + 1)\ln{8}$

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

c $A LaTex expression showing (t + 9)\ln{9} = (t )\ln{8}$

Use the power rule to simplify this equation

A LaTex expression showing 10 to the power of (r + 5) = 2 to the power of (r )

a $A LaTex expression showing (r + 5)\ln{10} = (r )\ln{2}$

b $A LaTex expression showing (5r + 1)\ln{10} = (2r + 1)\ln{2}$

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

Use the power rule to simplify this equation

A LaTex expression showing 4 to the power of (w + 6) = 10 to the power of (w )

a $A LaTex expression showing (6w + 1)\ln{4} = (2w + 1)\ln{10}$

b $A LaTex expression showing (w + 6)\ln{4} = (w )\ln{10}$

c $A LaTex expression showing (w - 6)\ln{4} = (w - 2)\ln{10}$

Use the power rule to simplify this equation

A LaTex expression showing 4 to the power of (p + 3) = 10 to the power of (p )

a $A LaTex expression showing (3p + 1)\ln{4} = (2p + 1)\ln{10}$

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

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

Use the power rule to simplify this equation

A LaTex expression showing 3 to the power of (q + 4) = 4 to the power of (q )

a $A LaTex expression showing (4q + 1)\ln{3} = (2q + 1)\ln{4}$

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

c $A LaTex expression showing (q + 4)\ln{3} = (q )\ln{4}$

Use the power rule to simplify this equation

A LaTex expression showing 3 to the power of (w + 7) = 2 to the power of (w )

a $A LaTex expression showing (w + 7)\ln{3} = (w )\ln{2}$

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

c $A LaTex expression showing (7w + 1)\ln{3} = (2w + 1)\ln{2}$

Use the power rule to simplify this equation

A LaTex expression showing 8 to the power of (t - 9) = 10 to the power of (t )

a $A LaTex expression showing (-9t + 1)\ln{8} = (2t + 1)\ln{10}$

b $A LaTex expression showing (t + 9)\ln{8} = (t - 2)\ln{10}$

c $A LaTex expression showing (t - 9)\ln{8} = (t )\ln{10}$