1.2.5 Logarithm

Question 1

If no log is stated what is it assumed to be?

Answer 1

10

Question 2

What is the log?

Answer 2

The power by which you times the base by?

Question 3

What happens if the base and the bracket are the same?

Answer 3

=1

Question 4

What is Log(1)?

Answer 4

0

Question 5

What is Log(10)?

Answer 5

1

Question 6

What is Log(100)?

Answer 6

2

Question 7

What is Log(1000)?

Answer 7

3 because 1000 is 10³

Question 8

What is Log(0.1)?

Answer 8

-1

Question 9

What is Log(0.01)?

Answer 9

-2

Question 10

What is Log(0.001)?

Answer 10

-3

Question 11

What is Log 3 (9)?

Answer 11

2 because 3² is 9.

Question 12

What is Log 9 (3)?

Answer 12

1/2 because anytime the log is larger than the brackets the answer is a fraction.

Question 13

What is Log 3 (1/9)?

Answer 13

-2 because anytime the brackets are a fraction the answer will be a negative.

Question 14

What is Log 2 (32)?

Answer 14

5 (2x2x2x2x2)

Question 15

What is Log 2 (1/32)?

Answer 15

-5

Question 16

What is Log 32 (2)?

Answer 16

1/5

Question 17

What is Log 32 (1/2)?

Answer 17

-1/5.

Question 18

What two parts does a logarithm consist of?

Answer 18

The whole number called the characteristic and the decimal part called the mantissa.

Question 19

How do you use log tables to get the log of 4.938?

Answer 19

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.

Question 20

What do you do to numbers outside the range 1-10?

Answer 20

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

Question 21

Once you have the number in a 1-10 range what do you do with the powers once you have worked out the log?

Answer 21

Add them together. Log 1.523 = 0.1826

1523= 10⁰.¹⁸²⁶ x 10³ = 10³.¹⁸²⁶

Question 22

If an antilog is 2.7312 what happens with the 2?

Answer 22

Remove it temporarily to work out the logarithm, then use to work out the decimal point.

Question 23

What is it key to remember if a logarithm number before the decimal point has a line above it?

Answer 23

That it is a minus meaning the decimal point will move to the left.

Question 24

What must you do if you are multiplying logs?

Answer 24

Find the logs of the numbers together and add them together.