(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 (frac{y}{y + 101} = frac{11}{10010}) are in base two, solve for y.
Explanation
(a) (log 3.6 = log (frac{18}{5}))
(log 18 – log 5 = log (2 times 3^{2}) – log 5)
(log 2 + log 3^{2} – log 5 = log 2 + 2log 3 – log 5)
= (0.3010 + 2(0.4771) – 0.6990)
= (0.3010 + 0.9542 – 0.6990)
= (0.5562).
(b) (frac{y}{y + 101} = frac{11}{10010}) (all in base 2)
Cross multiplying,
(11(y + 101) = 10010y)
(11y + 1111 = 10010y)
(10010y – 11y = 1111)
(1111y = 1111)
(y = 1).