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1 vote
If log103 0.4771,
evaluate log100.0003.
Round your answer to four decimal
places.

If log103 0.4771, evaluate log100.0003. Round your answer to four decimal places.-example-1
User Empire
by
4.1k points

1 Answer

5 votes

Answer:

log(0.0003) = -3.5229

Explanation:

The rules of logarithms tell you ...

log(ab) = log(a) +log(b)

Application

log(0.0003) = log(3×10^-4) = log(3) +log(10^-4)

= log(3) -4 = 0.4771 -4

log(0.0003) = -3.5229

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Additional comment

If you do much work with logarithms, you find that negative logarithms are generally expressed using a positive mantissa with a negative add-on. Often, that negative add-on is -9, so this would be ...

5.4771-9

This helps when taking antilogs, as you look up 0.4771 in the table to see that the multiplier is 3.

If you were to look up 0.5229, you would find 3.333, meaning the multiplier is 1/3.333 and the antilog of -3.5229 is (10^-3)/3.333. This may not be a convenient value to work with.

User Stephen Price
by
4.4k points