Theory question 101
Logarithms(a) Simplify, without using Mathematical tables: log10(30/16) − 2log10(5/9) + log10(400/243)
(b) Without using Mathematical tables, calculate √(P/Q) where P = 3.6 × 10−3 and Q = 2.25 × 106, leaving your answer in standard form.
Show the model answer
Model answer
(a) 2log(5/9) = log(25/81)
Expression = log[(30/16) ÷ (25/81) × (400/243)] = log[(30/16) × (81/25) × (400/243)]
= log1010 = 1
(b) P/Q = 3.6 × 10−3 ÷ (2.25 × 106) = 1.6 × 10−9 = 16 × 10−10
√(P/Q) = 4 × 10−5
Explanation
Make the power of ten even before taking the square root.