“Teach me,” she said.

[Cecily]

Logarithm quotient rule

The logarithm of the division of x and y is the difference of logarithm of x and logarithm of y.
logb(x / y) = logb(x) - logb(y)


so 10^7 = 10,000,000 = log 7
10^4 = 10,000 = log 4


log 7 - log 4 = log 3


Not sure what the (3.3 x) refers to but just taking their word for it


3.3 x 3 = 9.9


240/9.9 = 24 and change rounded down


I'm starting to figure this out but god dammit logs hurt my head.



Control
500 ml of cottage cheese was inoculated with a 2 ml culture of Pseudomonas aeruginosa and incubated at 25°C. Five hours after inoculation, in a standard plate count there were 200 bacterial cells/ml. After 29 hours at 25°C, there were 1,000,000 cells/ml.


Experiment
500 ml of cottage cheese containing the preservative was inoculated with a 2 ml culture of Pseudomonas aeruginosa. After 6 hours of incubation at 25°C, a standard plate count was performed. There were 700 bacterial cells/ml. After 38 hours, there were 61,000,000
bacterial cells/ml.


Number Log
1 0.00
2 0.30
5 0.70
6 0.78
24 1.38
32 1.51
200 2.30
700 2.85
1.00 × 106 6.00
6.10 × 106 6.79
6.10 × 107 7.79