Mr Daniels Maths
Solving Equations with indices

Set 1

Set 2

Set 3

Q1) Solve \(8^{5 x -2} = 8^{8}\). x= [ 2]

Q1) Solve \(3^{8x + 17} = 27^{6}\). x= [ \(\frac{1}{8}\)]

Q1) Solve \(5^{10x + 10} = 625^{7x -4}\) . x= [ 1\(\frac{4}{9}\)]

Q2) Solve \(9^{5 x -10} = 9^{10}\). x= [ 4]

Q2) Solve \(3^{9x + 20} = 81^{-10}\). x= [ -6\(\frac{2}{3}\)]

Q2) Solve \(5^{10x + 6} = 625^{3x -3}\) . x= [ 9]

Q3) Solve \(9^{2 x -2} = 9^{8}\). x= [ 5]

Q3) Solve \(2^{10x + 6} = 16^{-4}\). x= [ -2\(\frac{1}{5}\)]

Q3) Solve \(2^{5x + 3} = 32^{6x -8}\) . x= [ 1\(\frac{18}{25}\)]

Q4) Solve \(7^{8 x -10} = 7^{6}\). x= [ 2]

Q4) Solve \(4^{5x + 14} = 16^{-6}\). x= [ -5\(\frac{1}{5}\)]

Q4) Solve \(5^{7x + 3} = 125^{7x -2}\) . x= [ \(\frac{9}{14}\)]

Q5) Solve \(4^{10 x -7} = 4^{3}\). x= [ 1]

Q5) Solve \(3^{5x + 7} = 27^{-3}\). x= [ -3\(\frac{1}{5}\)]

Q5) Solve \(3^{7x + 4} = 243^{6x -6}\) . x= [ 1\(\frac{11}{23}\)]

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

Q6) Solve \(3^{10x + 9} = 27^{-8}\). x= [ -3\(\frac{3}{10}\)]

Q6) Solve \(5^{10x + 2} = 3125^{6x + 2}\) . x= [ -\(\frac{2}{5}\)]

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

Q7) Solve \(5^{7x + 16} = 625^{-7}\). x= [ -6\(\frac{2}{7}\)]

Q7) Solve \(4^{10x + 5} = 256^{8x -10}\) . x= [ 2\(\frac{1}{22}\)]

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

Q8) Solve \(5^{10x + 19} = 25^{5}\). x= [ -\(\frac{9}{10}\)]

Q8) Solve \(4^{5x + 6} = 256^{8x -8}\) . x= [ 1\(\frac{11}{27}\)]

Q9) Solve \(8^{3 x +7} = 8^{10}\). x= [ 1]

Q9) Solve \(4^{6x + 2} = 256^{8}\). x= [ 5]

Q9) Solve \(5^{5x + 9} = 3125^{7x -10}\) . x= [ 1\(\frac{29}{30}\)]

Q10) Solve \(5^{2 x +5} = 5^{7}\). x= [ 1]

Q10) Solve \(2^{9x + 17} = 8^{4}\). x= [ -\(\frac{5}{9}\)]

Q10) Solve \(5^{7x + 8} = 3125^{9x -10}\) . x= [ 1\(\frac{10}{19}\)]