First, write the number in scientific notation:
0.0000273 = 2.73×10–5
Taking the log:
log(0.0000273) = log(2.73 ×10–5)
The log of a product is equal to the sum of the logs of each multiplier, so
log(2.73 ×10–5) = log(2.73) + log(10–5)
log(2.73) = 0.436: the answer has three significant figures, reflecting the possible error in the last digit of 2.73.
log(10–5) = –5.000000000...: the answer has an infinite number of significant digits because 10–5 is an exact number and has no error.
Then,
log(2.73×10–5) = log(2.73) + log(10–5) = 0.436 + (–5.00000000...)
I'd rather do that shit, then read and write a paper any day all day