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

Level 1

This math topic focuses on solving exponential equations using logarithms, specifically employing the power property. It involves isolating the variable within an exponent in equations setup as one polynomial or binomial equaling another. Each problem provides an equation with exponential terms and asks to solve for a variable such as 'z', 'n', 'p', 't', 'r', 'w', and 'y'. Solutions are derived using natural logarithms (ln) to facilitate solving the exponent. These problems serve as advanced exercises in working with logarithmic functions and algebraic manipulation involving exponents.

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 1) to Answer Worksheet

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

Use the power rule to simplify this and solve for 'z'

A LaTex expression showing 3 to the power of (z + 4) = 8 to the power of (z )

a $A LaTex expression showing z=\frac{ -4\ln{3}}{ \ln{3} - \ln{8}}$

b $A LaTex expression showing z=\frac{ \ln{8} - \ln{3}}{ 4\ln{3} - 2\ln{8}}$

c $A LaTex expression showing z=\frac{ -4\ln{8}}{ \ln{8} - \ln{3}}$

Use the power rule to simplify this and solve for 'n'

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

a $A LaTex expression showing n=\frac{ -2\ln{10}}{ \ln{10} - \ln{2}}$

b $A LaTex expression showing n=\frac{ \ln{2} - \ln{10}}{ 2\ln{10} - 2\ln{2}}$

c $A LaTex expression showing n=\frac{ -2\ln{2}}{ \ln{2} - \ln{10}}$

Use the power rule to simplify this and solve for 'p'

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

a $A LaTex expression showing p=\frac{ -3\ln{2}}{ \ln{2} - \ln{7}}$

b $A LaTex expression showing p=\frac{ \ln{7} - \ln{2}}{ 3\ln{2} - 2\ln{7}}$

c $A LaTex expression showing p=\frac{ -3\ln{7}}{ \ln{7} - \ln{2}}$

Use the power rule to simplify this and solve for 't'

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

a $A LaTex expression showing t=\frac{ \ln{8} - \ln{10}}{ 8\ln{10} - 2\ln{8}}$

b $A LaTex expression showing t=\frac{ -8\ln{8}}{ \ln{8} - \ln{10}}$

c $A LaTex expression showing t=\frac{ -8\ln{10}}{ \ln{10} - \ln{8}}$

Use the power rule to simplify this and solve for 'r'

A LaTex expression showing 5 to the power of (r + 7) = 8 to the power of (r )

a $A LaTex expression showing r=\frac{ -7\ln{8}}{ \ln{8} - \ln{5}}$

b $A LaTex expression showing r=\frac{ \ln{8} - \ln{5}}{ 7\ln{5} - 2\ln{8}}$

c $A LaTex expression showing r=\frac{ -7\ln{5}}{ \ln{5} - \ln{8}}$

Use the power rule to simplify this and solve for 'w'

A LaTex expression showing 8 to the power of (w + 8) = 3 to the power of (w )

a $A LaTex expression showing w=\frac{ -8\ln{3}}{ \ln{3} - \ln{8}}$

b $A LaTex expression showing w=\frac{ -8\ln{8}}{ \ln{8} - \ln{3}}$

c $A LaTex expression showing w=\frac{ \ln{3} - \ln{8}}{ 8\ln{8} - 2\ln{3}}$

Use the power rule to simplify this and solve for 'y'

A LaTex expression showing 4 to the power of (y + 2) = 8 to the power of (y )

a $A LaTex expression showing y=\frac{ -2\ln{8}}{ \ln{8} - \ln{4}}$

b $A LaTex expression showing y=\frac{ -2\ln{4}}{ \ln{4} - \ln{8}}$

c $A LaTex expression showing y=\frac{ \ln{8} - \ln{4}}{ 2\ln{4} - 2\ln{8}}$

Use the power rule to simplify this and solve for 'r'

A LaTex expression showing 2 to the power of (r - 1) = 3 to the power of (r )

a $A LaTex expression showing r=\frac{ \ln{2}}{ \ln{2} - \ln{3}}$

b $A LaTex expression showing r=\frac{ \ln{3} - \ln{2}}{ -1\ln{2} - 2\ln{3}}$

c $A LaTex expression showing r=\frac{ \ln{3}}{ \ln{3} - \ln{2}}$