Theory question 106
Logarithms(a) if log10(3x − 1) − log102 = 3, find the value x.
(b) Use logarithm tables to evaluate √(0.897 × 3.536)/0.00249, correct to 3 significant figures
Show the model answer
Model answer
(a) log10((3x − 1)/2) = 3, so (3x − 1)/2 = 1000
3x − 1 = 2000, x = 2001/3 = 667
(b) log 0.897 = 1̄.9528, log 3.536 = 0.5485; sum = 0.5013
÷ 2 for the square root: 0.2507 (antilog ≈ 1.781)
Subtract log 0.00249 = 3̄.3962: 0.2507 − 3̄.3962 = 2.8545
Antilog = 715 (3 s.f.)
Explanation
Take the square root by halving the log before dividing by 0.00249.