1.2.5 Logarithm Flashcards
If no log is stated what is it assumed to be?
10
What is the log?
The power by which you times the base by?
What happens if the base and the bracket are the same?
=1
What is Log(1)?
0
What is Log(10)?
1
What is Log(100)?
2
What is Log(1000)?
3 because 1000 is 10³
What is Log(0.1)?
-1
What is Log(0.01)?
-2
What is Log(0.001)?
-3
What is Log 3 (9)?
2 because 3² is 9.
What is Log 9 (3)?
1/2 because anytime the log is larger than the brackets the answer is a fraction.
What is Log 3 (1/9)?
-2 because anytime the brackets are a fraction the answer will be a negative.
What is Log 2 (32)?
5 (2x2x2x2x2)
What is Log 2 (1/32)?
-5
What is Log 32 (2)?
1/5
What is Log 32 (1/2)?
-1/5.
What two parts does a logarithm consist of?
The whole number called the characteristic and the decimal part called the mantissa.
How do you use log tables to get the log of 4.938?
Go down the first column and find 49 (4.9), move along the row until you get to three (4.93) and take this number (.6928), then move to the right and use the fourth number 8 (4.938) to find the last number which is 7. So 4.938= 0.6928 + 0.0007 = 0.6935.
What do you do to numbers outside the range 1-10?
Put a decimal place in, depending how much you move the decimal point is how much the power becomes. E.g. 1523 = 1.523 x 10³ or 0.4621 becomes 4.621 x 10¯¹
Once you have the number in a 1-10 range what do you do with the powers once you have worked out the log?
Add them together. Log 1.523 = 0.1826
1523= 10⁰.¹⁸²⁶ x 10³ = 10³.¹⁸²⁶
If an antilog is 2.7312 what happens with the 2?
Remove it temporarily to work out the logarithm, then use to work out the decimal point.
What is it key to remember if a logarithm number before the decimal point has a line above it?
That it is a minus meaning the decimal point will move to the left.
What must you do if you are multiplying logs?
Find the logs of the numbers together and add them together.
