Theory question 102
Logarithms(a) Using logarithm table, evaluate ∛1.376/∜0.007 correct to three s.f.
(b) Without using Mathematical tables, find the value of (log 81)/(log 1/3)
Show the model answer
Model answer
(a) log 1.376 = 0.1386; ÷ 3 = 0.0462
log 0.007 = 3̄.8451; ÷ 4 = (4̄ + 1.8451) ÷ 4 = 1̄.4613
0.0462 − 1̄.4613 = 0.5849
antilog 0.5849 = 3.845 ≈ 3.85
(b) log 81 = 4 log 3 and log 1/3 = −log 3, so the value is 4 log 3/(−log 3) = −4
Explanation
To divide a negative characteristic by 4, first make it exactly divisible: 3̄.8451 = 4̄ + 1.8451.