Aim- Using the Common Log Table to multiply, divide, raise to powers and extract roots

Do Now: (without a calc)

1] 3520*843

2] 10^3.5465 * 10^2.9258 = 10^?

3] (10^3.5465)^1/2 = 10^?

4) sqrt{3520}

Above is a Logarithm Table that we will be using to complete our do now.

To do the Do Now efficiently, we need to learn how to use the Logarithm Table. The table above is better than the sheet we have because the decimal points are already put in for us. 6117 is actually .6117 and 40th row 3rd column is actually 4.03. Row means the numbers on the left side and middle going up and down, while the columns are the numbers on the top going left to right. The numbers inside will always be the exponents and the numbers on the rows and columns will always be the result.

Take a look at Row 3.1, Column 6. The result is .4997.
In mathematical terms,
10^.4997= 3.16
Note that .4997 is not equal to 3.16. It is 10^.4997.

Look at the 17th row, 8th column. The result is .2504.
That is equivalent to
10^.2504 = 1.78

What is the Log of 10^.3118 =?
We find .3118 in the 20th row, 5th column.
Log of 10^.3118 = 2.05.

10^x = 2.19
Let's work backwards now. 2.19 means 21st row, 9th column.
We find that .3404 is the value for the 21st row, 9th column.
As a result,
10^.3404 = 2.19

/sqrt{10}
The square root of 10 can be written is

10^1/2
1/2 = .5
We find .5 in the chart. It is closest to the 31st row, 6th column.
/sqrt{10} = 3.16

/sqrt{/sqrt{10}} = 10^.25 = ?
17th row 8th column will produce you .25.
10^.25 = 1.78

10^ .75 =
56th row 2nd column will produce you .75
10^ .75 = 5.62

Now here come's the harder part.
10^4.3118 =
This can be written as 10^4 * 10^.3118
Find .3118 in the chart, which is 20th row, 5th column. However, the answer is not 2.05. There is a 10^4. Multiply 2.05 by 10^4, and you will get 20500. To check, make sure that 20500 is between 10^4 (which is one of your exponents) and 10^5. If so, your answer is correct.
10^4 * 10^.3118 = 20500

10^x = 219,000,000
This equals 10^8 * 2.19.
Find out that 2.19 is 21st row, 9th column, which produces .3404.
The answer is 8.3404 because you add the 8, which is the exponent in front.
Check it:
10^8.3404 = 219,000,000.
10^8 * 10^.3404 = 219,000,000.
10^8 * 2.19 = 219,000,000.
219,000,000. = 219,000,000.

Let's do Number 1 of the Do Now now.
3520 * 843
What is 3520 and 843 equivalent to?
Find the values for 35th row, 2nd column, and 84th row, and 3rd column.
3520 can be written as 10^3.5465 and 843 can be written as 10^2.9258.
Due to the Law of Exponents, add the exponents together and you will get 10^6.4723.
10^6 * 10^.4723
Look up .4723 and you will get 29th row, 7th column.
10^6 * 10^2.97= 2.97*10^6 = 2,970,000.

Number 2 on the Do Now, we just did it. It is the same answer as number 1.
2,970,000
Number 3 on the Do Now:
(10^3.5465)^1/2
Find out what 10^3.5465 is equivalent to, which is 35200.
Multiply 35200 by 1/2, which is 17600.
(10^3.5465)^1/2 = 17600

Number 4 on the Do Now:
/sqrt{3520}
Find the 35th row, 2nd column, which is .5465.
/sqrt{3520} = 10^3.5465.
35th row, 2nd column is equal to .5465, but it is 10 raised to the .5465 power. In addition, 3520 is 10^3 times greater than 3.52. As a result, the answer is 10^3.5465, with the 3 in front of the .5465 to move 3.520 (result from .5465) three spaces to the right.

Joke of the Day: There's a snake exhibit in the Central Park Zoo. As the snakes got older, they did not have any babies. Experts came in to see what the problem was, and they called in a mathematician to help. He asked people to cut down trees and to make a round table out of them. He put the snakes on the table. 9 months later, (or however long snakes need to give birth), there were baby snakes! Everyone was very astonished and amazed. They asked the expert how he did it. The expert replied that the snakes were adders, and that they needed a log table to multiply.

Aim- Using the Common Log Table to multiply, divide, raise to powers and extract rootsDo Now: (without a calc)1] 3520*843

2] 10^3.5465 * 10^2.9258 = 10^?

3] (10^3.5465)^1/2 = 10^?

4) sqrt{3520}

To do the Do Now efficiently, we need to learn how to use the Logarithm Table. The table above is better than the sheet we have because the decimal points are already put in for us. 6117 is actually .6117 and 40th row 3rd column is actually 4.03. Row means the numbers on the left side and middle going up and down, while the columns are the numbers on the top going left to right. The numbers inside will always be the exponents and the numbers on the rows and columns will always be the result.

Take a look at Row 3.1, Column 6. The result is .4997.

In mathematical terms,

10^.4997= 3.16

Note that .4997 is not equal to 3.16. It is 10^.4997.

Look at the 17th row, 8th column. The result is .2504.

That is equivalent to

10^.2504 = 1.78

What is the Log of 10^.3118 =?

We find .3118 in the 20th row, 5th column.

Log of 10^.3118 = 2.05.

10^x = 2.19

Let's work backwards now. 2.19 means 21st row, 9th column.

We find that .3404 is the value for the 21st row, 9th column.

As a result,

10^.3404 = 2.19

/sqrt{10}

The square root of 10 can be written is

10^1/2

1/2 = .5

We find .5 in the chart. It is closest to the 31st row, 6th column.

/sqrt{10} = 3.16

/sqrt{/sqrt{10}} = 10^.25 = ?

17th row 8th column will produce you .25.

10^.25 = 1.78

10^ .75 =

56th row 2nd column will produce you .75

10^ .75 = 5.62

Now here come's the harder part.

10^4.3118 =

This can be written as 10^4 * 10^.3118

Find .3118 in the chart, which is 20th row, 5th column. However, the answer is not 2.05. There is a 10^4. Multiply 2.05 by 10^4, and you will get 20500. To check, make sure that 20500 is between 10^4 (which is one of your exponents) and 10^5. If so, your answer is correct.

10^4 * 10^.3118 = 20500

10^x = 219,000,000

This equals 10^8 * 2.19.

Find out that 2.19 is 21st row, 9th column, which produces .3404.

The answer is 8.3404 because you add the 8, which is the exponent in front.

Check it:

10^8.3404 = 219,000,000.

10^8 * 10^.3404 = 219,000,000.

10^8 * 2.19 = 219,000,000.

219,000,000. = 219,000,000.

Let's do Number 1 of the Do Now now.

3520 * 843

What is 3520 and 843 equivalent to?

Find the values for 35th row, 2nd column, and 84th row, and 3rd column.

3520 can be written as 10^3.5465 and 843 can be written as 10^2.9258.

Due to the Law of Exponents, add the exponents together and you will get 10^6.4723.

10^6 * 10^.4723

Look up .4723 and you will get 29th row, 7th column.

10^6 * 10^2.97= 2.97*10^6 = 2,970,000.

Number 2 on the Do Now, we just did it. It is the same answer as number 1.

2,970,000

Number 3 on the Do Now:

(10^3.5465)^1/2

Find out what 10^3.5465 is equivalent to, which is 35200.

Multiply 35200 by 1/2, which is 17600.

(10^3.5465)^1/2 = 17600

Number 4 on the Do Now:

/sqrt{3520}

Find the 35th row, 2nd column, which is .5465.

/sqrt{3520} = 10^3.5465.

35th row, 2nd column is equal to .5465, but it is 10 raised to the .5465 power. In addition, 3520 is 10^3 times greater than 3.52.

As a result, the answer is 10^3.5465, with the 3 in front of the .5465 to move 3.520 (result from .5465) three spaces to the right.

Joke of the Day:

There's a snake exhibit in the Central Park Zoo. As the snakes got older, they did not have any babies. Experts came in to see what the problem was, and they called in a mathematician to help. He asked people to cut down trees and to make a round table out of them. He put the snakes on the table. 9 months later, (or however long snakes need to give birth), there were baby snakes! Everyone was very astonished and amazed. They asked the expert how he did it. The expert replied that the snakes were adders, and that they needed a log table to multiply.

Frankie Choi

Period 10