 
Use this method if the bases are the same, or can be changed so they are the same. example 1: The bases are already the same 46x = 42x - 8 The exponents must also be the same. 6x = 2x - 8 Equate the exponents and solve. 4x = - 8 x = - 2 example 2: Again the bases are already the same 7x2 = 76 - x Equate the exponents and solve. x2 = 6 - x x2 + x - 6 = 0 This is a quadratic equation that can be solved by factoring. (x + 3)(x - 2) = 0 x = - 3 or x = 2 There are two answers. example 3: The bases are not the same. But we can make them the same ... 2x = 8x + 1 This is where memorizing simple powers (Math 9) will help. 2x = (23)x + 1 Change 8 to 23 2x = 23x + 3 Simplify. Since the bases are now equal, so are the exponents x = 3x + 3 Equate the exponents and solve - 2x = 3 x = - 3/2 or - 1.5 example 4: The bases are not the same, but we can make them the same by changing both 45 - 2x = 8x + 4 (22)5 - 2x = (23)x + 4 Both are powers of 2 210 - 4x = 23x + 12 Simplify. Since the bases are now equal, so are the exponents 10 - 4x = 3x + 12 Equate the exponents and solve - 7x = 2 x = - 2/7 or - 0.29 (rounded to 2 dp) |