Mr Daniels Maths
Solving Equations with indices

Set 1

Set 2

Set 3

Q1) Solve \(6^{10 x -10} = 6^{10}\). x= [ 2]

Q1) Solve \(4^{9x + 3} = 16^{5}\). x= [ \(\frac{7}{9}\)]

Q1) Solve \(4^{3x + 3} = 1024^{7x + 3}\) . x= [ -\(\frac{3}{8}\)]

Q2) Solve \(5^{8 x -6} = 5^{2}\). x= [ 1]

Q2) Solve \(2^{4x + 17} = 16^{8}\). x= [ 3\(\frac{3}{4}\)]

Q2) Solve \(3^{2x + 10} = 9^{2x + 7}\) . x= [ -2]

Q3) Solve \(7^{8 x -5} = 7^{3}\). x= [ 1]

Q3) Solve \(5^{6x + 15} = 25^{-4}\). x= [ -3\(\frac{5}{6}\)]

Q3) Solve \(3^{4x + 2} = 27^{5x + 2}\) . x= [ -\(\frac{4}{11}\)]

Q4) Solve \(7^{5 x -2} = 7^{8}\). x= [ 2]

Q4) Solve \(2^{5x + 1} = 16^{2}\). x= [ 1\(\frac{2}{5}\)]

Q4) Solve \(2^{4x + 2} = 4^{8x + 2}\) . x= [ -\(\frac{1}{6}\)]

Q5) Solve \(6^{7 x +3} = 6^{10}\). x= [ 1]

Q5) Solve \(5^{3x + 6} = 25^{-5}\). x= [ -5\(\frac{1}{3}\)]

Q5) Solve \(3^{3x + 7} = 81^{5x -9}\) . x= [ 2\(\frac{9}{17}\)]

Q6) Solve \(7^{9 x -9} = 7^{9}\). x= [ 2]

Q6) Solve \(4^{6x + 8} = 256^{-2}\). x= [ -2\(\frac{2}{3}\)]

Q6) Solve \(3^{7x + 1} = 81^{3x + 8}\) . x= [ -6\(\frac{1}{5}\)]

Q7) Solve \(2^{3 x -2} = 2^{10}\). x= [ 4]

Q7) Solve \(5^{7x + 2} = 25^{8}\). x= [ 2]

Q7) Solve \(5^{2x + 6} = 3125^{6x + 4}\) . x= [ -\(\frac{1}{2}\)]

Q8) Solve \(2^{4 x -3} = 2^{9}\). x= [ 3]

Q8) Solve \(2^{9x + 19} = 4^{-3}\). x= [ -2\(\frac{7}{9}\)]

Q8) Solve \(2^{7x + 6} = 8^{4x -3}\) . x= [ 3]

Q9) Solve \(5^{3 x -8} = 5^{10}\). x= [ 6]

Q9) Solve \(2^{5x + 14} = 8^{-8}\). x= [ -7\(\frac{3}{5}\)]

Q9) Solve \(3^{10x + 5} = 81^{2x -8}\) . x= [ -18\(\frac{1}{2}\)]

Q10) Solve \(6^{4 x -9} = 6^{7}\). x= [ 4]

Q10) Solve \(2^{6x + 11} = 16^{10}\). x= [ 4\(\frac{5}{6}\)]

Q10) Solve \(5^{2x + 7} = 125^{5x -6}\) . x= [ 1\(\frac{12}{13}\)]