Mr Daniels Maths
Solving Equations with indices

Set 1

Set 2

Set 3

Q1) Solve \(9^{4 x -10} = 9^{2}\). x= [ 3]

Q1) Solve \(4^{4x + 7} = 64^{6}\). x= [ 2\(\frac{3}{4}\)]

Q1) Solve \(3^{8x + 4} = 9^{10x -4}\) . x= [ 1]

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

Q2) Solve \(3^{5x + 15} = 27^{2}\). x= [ -1\(\frac{4}{5}\)]

Q2) Solve \(4^{10x + 2} = 1024^{3x -10}\) . x= [ 10\(\frac{2}{5}\)]

Q3) Solve \(5^{2 x -6} = 5^{10}\). x= [ 8]

Q3) Solve \(5^{2x + 1} = 125^{-4}\). x= [ -6\(\frac{1}{2}\)]

Q3) Solve \(4^{6x + 1} = 1024^{9x -2}\) . x= [ \(\frac{11}{39}\)]

Q4) Solve \(5^{6 x +4} = 5^{10}\). x= [ 1]

Q4) Solve \(2^{3x + 18} = 4^{3}\). x= [ -4]

Q4) Solve \(2^{6x + 8} = 16^{4x + 7}\) . x= [ -2]

Q5) Solve \(2^{8 x -10} = 2^{6}\). x= [ 2]

Q5) Solve \(4^{6x + 4} = 16^{9}\). x= [ 2\(\frac{1}{3}\)]

Q5) Solve \(4^{2x + 6} = 64^{3x -8}\) . x= [ 4\(\frac{2}{7}\)]

Q6) Solve \(3^{2 x +6} = 3^{10}\). x= [ 2]

Q6) Solve \(3^{3x + 14} = 27^{-10}\). x= [ -14\(\frac{2}{3}\)]

Q6) Solve \(3^{5x + 3} = 243^{6x + 7}\) . x= [ -1\(\frac{7}{25}\)]

Q7) Solve \(7^{2 x -10} = 7^{4}\). x= [ 7]

Q7) Solve \(5^{9x + 20} = 625^{-10}\). x= [ -6\(\frac{2}{3}\)]

Q7) Solve \(5^{5x + 3} = 3125^{4x + 9}\) . x= [ -2\(\frac{4}{5}\)]

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

Q8) Solve \(5^{5x + 15} = 625^{-2}\). x= [ -4\(\frac{3}{5}\)]

Q8) Solve \(2^{10x + 10} = 32^{4x -6}\) . x= [ 4]

Q9) Solve \(2^{7 x -5} = 2^{2}\). x= [ 1]

Q9) Solve \(2^{4x + 9} = 16^{-6}\). x= [ -8\(\frac{1}{4}\)]

Q9) Solve \(2^{5x + 5} = 32^{3x + 5}\) . x= [ -2]

Q10) Solve \(5^{7 x -8} = 5^{6}\). x= [ 2]

Q10) Solve \(3^{6x + 20} = 27^{7}\). x= [ \(\frac{1}{6}\)]

Q10) Solve \(4^{9x + 4} = 64^{5x -4}\) . x= [ 2\(\frac{2}{3}\)]