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

Level 1

This math topic practices solving logarithmic equations using the power property. It involves isolating the variable (like 'z' or 'p') in expressions where the variable is an exponent within logarithmic functions. The problems present equations with two binomial terms, where learners apply logarithmic algebra to derive solutions. Each problem involves simplification using logarithms to find the value of the variable, demonstrating an advanced understanding of logarithm properties. The examples include equations where bases and their exponents are manipulated algebraically to isolate and solve for the exponent, showcasing proficiency in handling logarithmic equations in algebra.

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, Two Binomials (Coefficient N) to Answer Worksheet

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

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

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

a $A LaTex expression showing z=\frac{ 9\ln{3} + 3\ln{6}}{ -3\ln{6} + 9\ln{3}}$

b $A LaTex expression showing z=\frac{ 9\ln{6} + 3\ln{3}}{ -3\ln{3} + 9\ln{6}}$

c $A LaTex expression showing z=\frac{ -9\ln{6} + 3\ln{3}}{ -3\ln{3} - 9\ln{6}}$

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

A LaTex expression showing 10 to the power of (-3p + 4) = 2 to the power of (-6p - 6)

a $A LaTex expression showing p=\frac{ -6\ln{10} - 4\ln{2}}{ -3\ln{2} + 6\ln{10}}$

b $A LaTex expression showing p=\frac{ -6\ln{2} - 4\ln{10}}{ -3\ln{10} + 6\ln{2}}$

c $A LaTex expression showing p=\frac{ -6\ln{2} + 3\ln{10}}{ 4\ln{10} + 6\ln{2}}$

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

A LaTex expression showing 7 to the power of (-1t + 2) = 4 to the power of (5t + 9)

a $A LaTex expression showing t=\frac{ 5\ln{4} + \ln{7}}{ 2\ln{7} - 9\ln{4}}$

b $A LaTex expression showing t=\frac{ 9\ln{7} - 2\ln{4}}{ -1\ln{4} - 5\ln{7}}$

c $A LaTex expression showing t=\frac{ 9\ln{4} - 2\ln{7}}{ -1\ln{7} - 5\ln{4}}$

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

A LaTex expression showing 7 to the power of (-3x + 9) = 5 to the power of (-9x - 4)

a $A LaTex expression showing x=\frac{ -4\ln{7} - 9\ln{5}}{ -3\ln{5} + 9\ln{7}}$

b $A LaTex expression showing x=\frac{ -9\ln{5} + 3\ln{7}}{ 9\ln{7} + 4\ln{5}}$

c $A LaTex expression showing x=\frac{ -4\ln{5} - 9\ln{7}}{ -3\ln{7} + 9\ln{5}}$

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

A LaTex expression showing 7 to the power of (-8r - 6) = 4 to the power of (-4r + 6)

a $A LaTex expression showing r=\frac{ 6\ln{7} + 6\ln{4}}{ -8\ln{4} + 4\ln{7}}$

b $A LaTex expression showing r=\frac{ -4\ln{4} + 8\ln{7}}{ -6\ln{7} - 6\ln{4}}$

c $A LaTex expression showing r=\frac{ 6\ln{4} + 6\ln{7}}{ -8\ln{7} + 4\ln{4}}$

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

A LaTex expression showing 5 to the power of (2p + 9) = 8 to the power of (2p + 9)

a $A LaTex expression showing p=\frac{ 2\ln{8} - 2\ln{5}}{ 9\ln{5} - 9\ln{8}}$

b $A LaTex expression showing p=\frac{ 9\ln{5} - 9\ln{8}}{ 2\ln{8} - 2\ln{5}}$

c $A LaTex expression showing p=\frac{ 9\ln{8} - 9\ln{5}}{ 2\ln{5} - 2\ln{8}}$

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

A LaTex expression showing 2 to the power of (7n - 1) = 7 to the power of (-5n - 6)

a $A LaTex expression showing n=\frac{ -6\ln{2} + 1\ln{7}}{ 7\ln{7} + 5\ln{2}}$

b $A LaTex expression showing n=\frac{ -5\ln{7} - 7\ln{2}}{ -1\ln{2} + 6\ln{7}}$

c $A LaTex expression showing n=\frac{ -6\ln{7} + \ln{2}}{ 7\ln{2} + 5\ln{7}}$

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

A LaTex expression showing 9 to the power of (-6p + 4) = 2 to the power of (p + 7)

a $A LaTex expression showing p=\frac{ 7\ln{9} - 4\ln{2}}{ -6\ln{2} - \ln{9}}$

b $A LaTex expression showing p=\frac{ 7\ln{2} - 4\ln{9}}{ -6\ln{9} - 1\ln{2}}$

c $A LaTex expression showing p=\frac{ \ln{2} + 6\ln{9}}{ 4\ln{9} - 7\ln{2}}$