Mr Daniels Maths
Solving Equations with indices

Easy

Medium

Difficult

Q1) Solve \(8^{3 x -7} = 8^{5}\). x= 4
Q1) Solve \(5^{3x + 11} = 625^{6}\). x= 4\(\frac{1}{3}\)
Q1) Solve \(4^{9x + 3} = 16^{9x -9}\) . x= 2\(\frac{1}{3}\)
Q2) Solve \(6^{3 x +4} = 6^{10}\). x= 2
Q2) Solve \(5^{6x + 11} = 25^{8}\). x= \(\frac{5}{6}\)
Q2) Solve \(2^{10x + 5} = 16^{3x + 3}\) . x= -3\(\frac{1}{2}\)
Q3) Solve \(3^{10 x -4} = 3^{6}\). x= 1
Q3) Solve \(2^{8x + 6} = 16^{-5}\). x= -3\(\frac{1}{4}\)
Q3) Solve \(3^{6x + 2} = 9^{8x -9}\) . x= 2
Q4) Solve \(2^{2 x +10} = 2^{2}\). x= -4
Q4) Solve \(3^{9x + 6} = 9^{-2}\). x= -1\(\frac{1}{9}\)
Q4) Solve \(2^{7x + 9} = 16^{9x -4}\) . x= \(\frac{25}{29}\)
Q5) Solve \(6^{3 x +4} = 6^{7}\). x= 1
Q5) Solve \(4^{6x + 8} = 16^{10}\). x= 2
Q5) Solve \(4^{10x + 7} = 16^{10x -6}\) . x= 1\(\frac{9}{10}\)
Q6) Solve \(3^{6 x +9} = 3^{3}\). x= -1
Q6) Solve \(4^{2x + 3} = 16^{5}\). x= 3\(\frac{1}{2}\)
Q6) Solve \(2^{9x + 1} = 4^{6x + 5}\) . x= -3
Q7) Solve \(4^{3 x +9} = 4^{6}\). x= -1
Q7) Solve \(4^{7x + 1} = 256^{-9}\). x= -5\(\frac{2}{7}\)
Q7) Solve \(3^{5x + 5} = 81^{5x -2}\) . x= \(\frac{13}{15}\)
Q8) Solve \(3^{6 x +8} = 3^{2}\). x= -1
Q8) Solve \(3^{10x + 13} = 81^{-8}\). x= -4\(\frac{1}{2}\)
Q8) Solve \(2^{7x + 2} = 16^{3x -3}\) . x= 2\(\frac{4}{5}\)
Q9) Solve \(8^{4 x -5} = 8^{7}\). x= 3
Q9) Solve \(5^{2x + 13} = 25^{6}\). x= -\(\frac{1}{2}\)
Q9) Solve \(3^{3x + 6} = 243^{5x + 5}\) . x= -\(\frac{19}{22}\)
Q10) Solve \(9^{3 x +9} = 9^{3}\). x= -2
Q10) Solve \(3^{10x + 17} = 27^{-7}\). x= -3\(\frac{4}{5}\)
Q10) Solve \(4^{3x + 5} = 256^{5x -7}\) . x= 1\(\frac{16}{17}\)