Mr Daniels Maths
Solving Equations with indices

Set 1

Set 2

Set 3

Q1) Solve \(7^{3 x -6} = 7^{3}\). x= [ 3]

Q1) Solve \(3^{5x + 16} = 9^{-7}\). x= [ -6]

Q1) Solve \(2^{5x + 3} = 4^{3x -6}\) . x= [ 15]

Q2) Solve \(6^{4 x -10} = 6^{6}\). x= [ 4]

Q2) Solve \(2^{5x + 13} = 8^{-7}\). x= [ -6\(\frac{4}{5}\)]

Q2) Solve \(3^{2x + 9} = 9^{6x + 7}\) . x= [ -\(\frac{1}{2}\)]

Q3) Solve \(8^{6 x -10} = 8^{2}\). x= [ 2]

Q3) Solve \(5^{8x + 13} = 125^{-8}\). x= [ -4\(\frac{5}{8}\)]

Q3) Solve \(5^{7x + 7} = 25^{3x + 6}\) . x= [ 5]

Q4) Solve \(2^{3 x +10} = 2^{4}\). x= [ -2]

Q4) Solve \(2^{4x + 16} = 16^{3}\). x= [ -1]

Q4) Solve \(4^{3x + 2} = 16^{9x + 2}\) . x= [ -\(\frac{2}{15}\)]

Q5) Solve \(2^{2 x -4} = 2^{10}\). x= [ 7]

Q5) Solve \(4^{3x + 12} = 16^{-7}\). x= [ -8\(\frac{2}{3}\)]

Q5) Solve \(5^{8x + 2} = 625^{7x + 8}\) . x= [ -1\(\frac{1}{2}\)]

Q6) Solve \(5^{5 x +5} = 5^{10}\). x= [ 1]

Q6) Solve \(2^{9x + 10} = 4^{9}\). x= [ \(\frac{8}{9}\)]

Q6) Solve \(4^{5x + 1} = 16^{6x -2}\) . x= [ \(\frac{5}{7}\)]

Q7) Solve \(5^{3 x -9} = 5^{3}\). x= [ 4]

Q7) Solve \(2^{8x + 13} = 4^{-2}\). x= [ -2\(\frac{1}{8}\)]

Q7) Solve \(2^{3x + 3} = 32^{4x -5}\) . x= [ 1\(\frac{11}{17}\)]

Q8) Solve \(8^{8 x -7} = 8^{9}\). x= [ 2]

Q8) Solve \(2^{3x + 10} = 8^{-4}\). x= [ -7\(\frac{1}{3}\)]

Q8) Solve \(4^{7x + 6} = 256^{8x + 9}\) . x= [ -1\(\frac{1}{5}\)]

Q9) Solve \(6^{5 x +10} = 6^{5}\). x= [ -1]

Q9) Solve \(4^{4x + 13} = 256^{-10}\). x= [ -13\(\frac{1}{4}\)]

Q9) Solve \(5^{6x + 5} = 25^{10x -8}\) . x= [ 1\(\frac{1}{2}\)]

Q10) Solve \(6^{2 x -8} = 6^{4}\). x= [ 6]

Q10) Solve \(2^{10x + 12} = 4^{-5}\). x= [ -2\(\frac{1}{5}\)]

Q10) Solve \(3^{2x + 8} = 243^{5x -9}\) . x= [ 2\(\frac{7}{23}\)]