Theory question 101
Logarithms(a) Without using calculator or tables, find the value of log 3.6 given that log 2 = 0.3010, log 3 = 0.4771 and log 5 = 0.6990.
(b) If all numbers in the equation y/(y + 101) = 11/10010 are in base two, solve for y.
Show the model answer
Model answer
(a) 3.6 = 18/5 = (2 × 32)/5.
log 3.6 = log 2 + 2 log 3 − log 5 = 0.3010 + 0.9542 − 0.6990 = 0.5562.
(b) In base ten: 101two = 5, 11two = 3, 10010two = 18.
y/(y + 5) = 3/18 → 18y = 3y + 15 → 15y = 15 → y = 1.
Explanation
Write 3.6 as a product and quotient of 2, 3 and 5.