Theory question 101
Indices(a) If 92x+1 = 81x−2/3x, find x.
(b) Without using Mathematical Tables, evaluate √((0.81 × 10−5)/(2.25 × 107))
Show the model answer
Model answer
(a) Write everything as powers of 3: 32(2x+1) = 34(x−2) ÷ 3x
So 4x + 2 = 4x − 8 − x = 3x − 8
x = −10
(b) (0.81 × 10−5)/(2.25 × 107) = (81/225) × 10−12 = 0.36 × 10−12
Square root: 0.6 × 10−6 = 6 × 10−7
Explanation
Turn both sides into the same base before comparing indices.