Mr Daniels Maths
Solving Equations with indices

Set 1

Set 2

Set 3

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

Q1) Solve \(2^{4x + 19} = 8^{10}\). x= [ 2\(\frac{3}{4}\)]

Q1) Solve \(4^{10x + 2} = 256^{6x + 9}\) . x= [ -2\(\frac{3}{7}\)]

Q2) Solve \(3^{4 x +3} = 3^{7}\). x= [ 1]

Q2) Solve \(5^{10x + 16} = 125^{-10}\). x= [ -4\(\frac{3}{5}\)]

Q2) Solve \(2^{6x + 4} = 4^{4x -9}\) . x= [ 11]

Q3) Solve \(3^{8 x -4} = 3^{4}\). x= [ 1]

Q3) Solve \(5^{2x + 15} = 125^{-3}\). x= [ -12]

Q3) Solve \(5^{7x + 3} = 125^{7x + 10}\) . x= [ -1\(\frac{13}{14}\)]

Q4) Solve \(9^{6 x -9} = 9^{3}\). x= [ 2]

Q4) Solve \(5^{2x + 4} = 125^{7}\). x= [ 8\(\frac{1}{2}\)]

Q4) Solve \(5^{8x + 10} = 3125^{4x -7}\) . x= [ 3\(\frac{3}{4}\)]

Q5) Solve \(3^{8 x -3} = 3^{5}\). x= [ 1]

Q5) Solve \(4^{7x + 16} = 16^{-2}\). x= [ -2\(\frac{6}{7}\)]

Q5) Solve \(4^{6x + 3} = 64^{5x + 8}\) . x= [ -2\(\frac{1}{3}\)]

Q6) Solve \(7^{7 x -9} = 7^{5}\). x= [ 2]

Q6) Solve \(5^{8x + 6} = 625^{-9}\). x= [ -5\(\frac{1}{4}\)]

Q6) Solve \(5^{3x + 10} = 625^{9x + 4}\) . x= [ -\(\frac{2}{11}\)]

Q7) Solve \(6^{2 x -5} = 6^{5}\). x= [ 5]

Q7) Solve \(3^{4x + 6} = 9^{-3}\). x= [ -3]

Q7) Solve \(4^{9x + 10} = 16^{5x + 8}\) . x= [ -6]

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

Q8) Solve \(4^{6x + 16} = 64^{-9}\). x= [ -7\(\frac{1}{6}\)]

Q8) Solve \(3^{7x + 6} = 243^{7x -9}\) . x= [ 1\(\frac{23}{28}\)]

Q9) Solve \(3^{5 x -6} = 3^{9}\). x= [ 3]

Q9) Solve \(5^{9x + 14} = 625^{-3}\). x= [ -2\(\frac{8}{9}\)]

Q9) Solve \(3^{8x + 5} = 81^{7x + 8}\) . x= [ -1\(\frac{7}{20}\)]

Q10) Solve \(4^{8 x -6} = 4^{10}\). x= [ 2]

Q10) Solve \(4^{6x + 16} = 16^{-6}\). x= [ -4\(\frac{2}{3}\)]

Q10) Solve \(4^{8x + 8} = 64^{4x + 6}\) . x= [ -2\(\frac{1}{2}\)]