Mr Daniels Maths
Solving Equations with indices

Set 1

Set 2

Set 3

Q1) Solve \(8^{5 x -10} = 8^{10}\). x= [ 4]

Q1) Solve \(3^{5x + 16} = 9^{2}\). x= [ -2\(\frac{2}{5}\)]

Q1) Solve \(3^{6x + 9} = 243^{8x -3}\) . x= [ \(\frac{12}{17}\)]

Q2) Solve \(6^{5 x +5} = 6^{10}\). x= [ 1]

Q2) Solve \(2^{5x + 4} = 8^{5}\). x= [ 2\(\frac{1}{5}\)]

Q2) Solve \(2^{7x + 4} = 8^{3x -2}\) . x= [ 5]

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

Q3) Solve \(5^{10x + 3} = 25^{3}\). x= [ \(\frac{3}{10}\)]

Q3) Solve \(2^{4x + 2} = 8^{4x + 8}\) . x= [ -2\(\frac{3}{4}\)]

Q4) Solve \(5^{3 x -8} = 5^{10}\). x= [ 6]

Q4) Solve \(3^{10x + 17} = 27^{6}\). x= [ \(\frac{1}{10}\)]

Q4) Solve \(2^{6x + 9} = 32^{6x -4}\) . x= [ 1\(\frac{5}{24}\)]

Q5) Solve \(7^{2 x +6} = 7^{4}\). x= [ -1]

Q5) Solve \(5^{9x + 6} = 25^{2}\). x= [ -\(\frac{2}{9}\)]

Q5) Solve \(4^{10x + 7} = 256^{6x -9}\) . x= [ 3\(\frac{1}{14}\)]

Q6) Solve \(5^{2 x -6} = 5^{2}\). x= [ 4]

Q6) Solve \(2^{5x + 7} = 16^{-4}\). x= [ -4\(\frac{3}{5}\)]

Q6) Solve \(5^{4x + 1} = 625^{10x -9}\) . x= [ 1\(\frac{1}{36}\)]

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

Q7) Solve \(4^{8x + 7} = 64^{-10}\). x= [ -4\(\frac{5}{8}\)]

Q7) Solve \(4^{3x + 4} = 64^{2x -8}\) . x= [ 9\(\frac{1}{3}\)]

Q8) Solve \(7^{6 x -4} = 7^{2}\). x= [ 1]

Q8) Solve \(4^{5x + 12} = 256^{2}\). x= [ -\(\frac{4}{5}\)]

Q8) Solve \(2^{6x + 3} = 8^{9x -8}\) . x= [ 1\(\frac{2}{7}\)]

Q9) Solve \(3^{10 x -4} = 3^{6}\). x= [ 1]

Q9) Solve \(4^{8x + 9} = 64^{-5}\). x= [ -3]

Q9) Solve \(5^{5x + 6} = 625^{8x + 7}\) . x= [ -\(\frac{22}{27}\)]

Q10) Solve \(8^{3 x +3} = 8^{9}\). x= [ 2]

Q10) Solve \(3^{5x + 4} = 27^{-4}\). x= [ -3\(\frac{1}{5}\)]

Q10) Solve \(3^{2x + 2} = 81^{10x + 8}\) . x= [ -\(\frac{15}{19}\)]