Mr Daniels Maths
Solving Equations with indices

Set 1

Set 2

Set 3

Q1) Solve \(6^{3 x +4} = 6^{10}\). x= [ 2]

Q1) Solve \(2^{2x + 7} = 8^{-6}\). x= [ -12\(\frac{1}{2}\)]

Q1) Solve \(2^{6x + 8} = 8^{3x -9}\) . x= [ 11\(\frac{2}{3}\)]

Q2) Solve \(5^{2 x -2} = 5^{4}\). x= [ 3]

Q2) Solve \(3^{8x + 3} = 27^{6}\). x= [ 1\(\frac{7}{8}\)]

Q2) Solve \(2^{4x + 2} = 4^{7x -3}\) . x= [ \(\frac{4}{5}\)]

Q3) Solve \(3^{7 x -8} = 3^{6}\). x= [ 2]

Q3) Solve \(5^{7x + 2} = 25^{-5}\). x= [ -1\(\frac{5}{7}\)]

Q3) Solve \(4^{6x + 5} = 16^{5x + 2}\) . x= [ \(\frac{1}{4}\)]

Q4) Solve \(2^{5 x -8} = 2^{7}\). x= [ 3]

Q4) Solve \(3^{3x + 11} = 27^{9}\). x= [ 5\(\frac{1}{3}\)]

Q4) Solve \(4^{8x + 1} = 16^{8x + 2}\) . x= [ -\(\frac{3}{8}\)]

Q5) Solve \(4^{8 x -9} = 4^{7}\). x= [ 2]

Q5) Solve \(5^{4x + 4} = 25^{4}\). x= [ 1]

Q5) Solve \(5^{8x + 5} = 25^{9x -2}\) . x= [ \(\frac{9}{10}\)]

Q6) Solve \(2^{2 x +4} = 2^{10}\). x= [ 3]

Q6) Solve \(5^{2x + 7} = 25^{-7}\). x= [ -10\(\frac{1}{2}\)]

Q6) Solve \(5^{9x + 7} = 625^{4x -3}\) . x= [ 2\(\frac{5}{7}\)]

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

Q7) Solve \(5^{7x + 6} = 625^{7}\). x= [ 3\(\frac{1}{7}\)]

Q7) Solve \(3^{8x + 7} = 9^{10x -9}\) . x= [ 2\(\frac{1}{12}\)]

Q8) Solve \(5^{2 x +9} = 5^{7}\). x= [ -1]

Q8) Solve \(3^{10x + 4} = 81^{-7}\). x= [ -3\(\frac{1}{5}\)]

Q8) Solve \(5^{5x + 10} = 3125^{10x + 10}\) . x= [ -\(\frac{8}{9}\)]

Q9) Solve \(2^{7 x +2} = 2^{9}\). x= [ 1]

Q9) Solve \(4^{8x + 14} = 64^{-9}\). x= [ -5\(\frac{1}{8}\)]

Q9) Solve \(2^{3x + 2} = 16^{4x + 5}\) . x= [ -1\(\frac{5}{13}\)]

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

Q10) Solve \(5^{3x + 6} = 25^{-4}\). x= [ -4\(\frac{2}{3}\)]

Q10) Solve \(2^{7x + 7} = 32^{9x + 7}\) . x= [ -\(\frac{14}{19}\)]