Logarithm help, please

Factual Questions
1

Hi everyone. An easy question if you know the answer, but insoluable if you’re me and you don’t.

My friend is being treated for Hepatitis C. She would like to know what log drop she has had in her viral load since beginning treatment (at least a 2 log base 10 drop is the target for 12 weeks of treatment).

She began treatment with a viral load of 3,510,000.
Her viral load now is 7,690.

  1. What log drop is this? (I assume a 2 log 10 drop would be a current viral load of 35,100 but I’m not sure that I have that right.)

  2. Can you provide me with a formula for tracking the drop over time?

Thank you.

2

log(3510000) = 6.54 and log(7690) = 3.89, so it sounds like she’s in good shape. If I have the epidemiology right, the equation is log(o/n), where o is the old viral load, and n is the new viral load.

3

If I understand correctly, a “log base 10 drop” is when the number goes down by a factor of 10, so essentially you lose a digit, like from 3,510,000 to 351,000. So, yes, you are right that “a 2 log 10 drop would be a current viral load of 35,100.”