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Lesson 63 · Counting log cycles
Logs, percents and the twelve-D cook
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Logs, percents and the twelve-D cook

The trade counts kill in logs, and the public reads it in percents. They are the same statement, and the conversion is worth knowing cold: P=1−10−LRP = 1 - 10^{-\mathrm{LR}} — P equals one minus ten to the minus L-R. PP is the fraction destroyed, running from 0 to 1 (multiply by 100 to say it as a percentage), and LR\mathrm{LR} is the log reduction, the bare count of powers of ten. The term 10−LR10^{-\mathrm{LR}} is the surviving fraction, which is what makes the identity readable: kill plus survivors is one.

The table is short and worth memorising. 1 log is 90%. 2 logs is 99%. 3 logs is 99.9%. 4 logs is 99.99%. For any claim written as a run of nines, the log reduction is the count of the nines.

Now the reason professionals prefer logs. Percentages crowd together at the top of the scale: 99% and 99.99% look almost identical written out, and differ by a factor of a hundred in survivors. Logs keep those apart, because each one is a whole step. And the two forms must never be added — writing "4-log removal plus 99.99% removal" counts a single barrier twice, which is a real and recurring error in treatment reports.

Going the other way, LR=−log⁡10(1−P)\mathrm{LR} = -\log_{10}(1 - P): take the survivors, take their logarithm, flip the sign. And to find what is actually left, N=N010 LRN = \dfrac{N_0}{10^{\,\mathrm{LR}}}, where N0N_0 is the count going in and NN the count coming out.

Which brings up the one thing a log reduction cannot tell you on its own: it is relative. Twelve logs from a starting load of 10310^{3} per can and twelve logs from 10610^{6} leave wildly different numbers of survivors. The incoming load matters as much as the process does, which is why raw-material hygiene is part of a thermal schedule and not a separate conversation.

The famous number in this field is 12D — the classic low-acid canning convention, twelve decimal reductions against the target spore. Read it as exactly what it says: twelve D-values laid end to end, t=12Dt = 12D. Nothing more mysterious than that, and nothing less demanding.

PLRN

P=1−10−LRP = 1 - 10^{-\mathrm{LR}}

  • PP= Percent kill
  • LR\mathrm{LR}= Log reduction
Log Reduction to Percent Kill solver →
DN/N0tLR

D=tLRD = \frac{t}{\mathrm{LR}}

  • DD= D-value (time)
  • tt= Holding time (time)
  • LR\mathrm{LR}= Log reduction achieved
D-Value (Decimal Reduction Time) solver →
N0NLR

LR=log⁡10 ⁣(N0N)\mathrm{LR} = \log_{10}\!\left(\frac{N_0}{N}\right)

  • LR\mathrm{LR}= Log reduction
  • N0N_0= Count before
  • NN= Count after
Log Inactivation from Counts solver →