Theory question 107
Logarithms(a) With the aid of four-figure logarithm tables, evaluate (0.004592)1/3.
(b) If log10y + 3log10x = 2, express y in terms of x.
(c) Solve the equations: 3x − 2y = 21; 4x + 5y = 5.
Show the model answer
Model answer
(a) log 0.004592 = 3̄.6620. Divide by 3: (−3 + 0.6620)/3 = 1̄.2207. Antilog = 0.1663.
(b) log(yx3) = 2, so yx3 = 100 and y = 100/x3.
(c) 15x − 10y = 105 and 8x + 10y = 10. Adding: 23x = 115, so x = 5; then 3(5) − 2y = 21 gives y = −3.
Explanation
When dividing a log with a negative characteristic, make the characteristic a multiple of 3 first.