Mr Daniels Maths
Solving Equations with indices

Set 1

Set 2

Set 3

Q1) Solve \(4^{2 x +2} = 4^{4}\). x= [ 1]

Q1) Solve \(4^{5x + 19} = 256^{8}\). x= [ 2\(\frac{3}{5}\)]

Q1) Solve \(4^{7x + 5} = 1024^{5x -10}\) . x= [ 3\(\frac{1}{18}\)]

Q2) Solve \(2^{2 x +8} = 2^{2}\). x= [ -3]

Q2) Solve \(5^{6x + 6} = 25^{-7}\). x= [ -3\(\frac{1}{3}\)]

Q2) Solve \(3^{10x + 6} = 27^{6x -5}\) . x= [ 2\(\frac{5}{8}\)]

Q3) Solve \(2^{5 x -7} = 2^{8}\). x= [ 3]

Q3) Solve \(4^{6x + 10} = 64^{-9}\). x= [ -6\(\frac{1}{6}\)]

Q3) Solve \(3^{5x + 3} = 243^{9x + 5}\) . x= [ -\(\frac{11}{20}\)]

Q4) Solve \(7^{9 x -9} = 7^{9}\). x= [ 2]

Q4) Solve \(3^{2x + 14} = 81^{-6}\). x= [ -19]

Q4) Solve \(5^{4x + 3} = 625^{5x -4}\) . x= [ 1\(\frac{3}{16}\)]

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

Q5) Solve \(5^{10x + 18} = 125^{9}\). x= [ \(\frac{9}{10}\)]

Q5) Solve \(3^{8x + 5} = 9^{10x + 4}\) . x= [ -\(\frac{1}{4}\)]

Q6) Solve \(3^{2 x -3} = 3^{9}\). x= [ 6]

Q6) Solve \(2^{5x + 13} = 16^{-9}\). x= [ -9\(\frac{4}{5}\)]

Q6) Solve \(2^{2x + 1} = 16^{6x -2}\) . x= [ \(\frac{9}{22}\)]

Q7) Solve \(9^{4 x +6} = 9^{10}\). x= [ 1]

Q7) Solve \(5^{8x + 1} = 625^{5}\). x= [ 2\(\frac{3}{8}\)]

Q7) Solve \(3^{4x + 6} = 27^{8x -2}\) . x= [ \(\frac{3}{5}\)]

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

Q8) Solve \(5^{5x + 14} = 625^{10}\). x= [ 5\(\frac{1}{5}\)]

Q8) Solve \(2^{5x + 8} = 8^{10x + 10}\) . x= [ -\(\frac{22}{25}\)]

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

Q9) Solve \(5^{4x + 2} = 25^{3}\). x= [ 1]

Q9) Solve \(2^{2x + 9} = 16^{2x -4}\) . x= [ 4\(\frac{1}{6}\)]

Q10) Solve \(5^{8 x -6} = 5^{2}\). x= [ 1]

Q10) Solve \(5^{7x + 7} = 625^{-4}\). x= [ -3\(\frac{2}{7}\)]

Q10) Solve \(5^{2x + 1} = 625^{3x + 8}\) . x= [ -3\(\frac{1}{10}\)]