Use the logrithm table to find the log of these numbers (a)900(b)4620(c)12.34
The log table gives the logs of numbers from 1-9.9999 or something
Now note that since
900 = 9 * 10^2
then
log900 = log9 + 2
so look up log9 and add 2
log4620 = log 4.62 + 3
and so on
ANSWER 4620 - 4.62 =2.859
To find the logarithm of these numbers using a logarithm table, we will be using the common logarithm (base 10). Here are the steps:
(a) Calculating the log of 900:
Looking up the value in the log table:
Log value of 90 = 1.9542
Adding 2 since 900 is 10^2 times larger than 90:
Log value of 900 = 1.9542 + 2 = 3.9542
Therefore, the log of 900 is approximately 3.9542.
(b) Calculating the log of 4620:
Looking up the values in the log table:
Log value of 46 = 1.6628
Adding 2 since 4620 is 10^2 times larger than 46:
Log value of 4600 = 1.6628 + 2 = 3.6628
Adding 0.02 since 20 is 10% of 200:
Log value of 4620 = 3.6628 + 0.02 = 3.6828
Therefore, the log of 4620 is approximately 3.6828.
(c) Calculating the log of 12.34:
Looking up the values in the log table:
Log value of 1.23 = 0.0899
Adding 1 since 12.34 is 10 times larger than 1.23:
Log value of 12.34 = 0.0899 + 1 = 1.0899
Adding 0.01 since 1.1 is 10% of 11:
Log value of 12.34 = 1.0899 + 0.01 = 1.0999
Therefore, the log of 12.34 is approximately 1.0999.
To find the logarithm of a number using a logarithm table, follow these steps:
Step 1: Look up the logarithm table:
First, you need to have a logarithm table. These tables are available in mathematics reference books or can be found online.
Step 2: Find the column for the appropriate base:
Logarithms are calculated with respect to a specific base. Common bases for logarithms are 10 (logarithm base 10) and e (natural logarithm). If your logarithm table is based on a different base, locate the corresponding column for that base.
Step 3: Locate the number in the table:
Find the row in the table that corresponds to the number for which you want to find the logarithm. Locate the appropriate column that matches the base.
Now let's proceed with finding the logarithm of the given numbers:
(a) To find the logarithm of 900:
- Assuming you are using a logarithm table with a base of 10, locate the column for base 10.
- Find the row that corresponds to the number 900.
- Read the value in the cell where the row and column intersect. This value is the logarithm of 900.
- Based on the logarithm table value, the logarithm of 900 (to base 10) is approximately 2.9542.
(b) To find the logarithm of 4620:
- Follow the same process as for part (a), but now locate the row that corresponds to 4620.
- Read the value in the column for base 10 (or the appropriate base of your logarithm table).
- Based on the logarithm table value, the logarithm of 4620 (to base 10) is approximately 3.6649.
(c) To find the logarithm of 12.34:
- If your logarithm table does not have values for decimal numbers, you can approximate the logarithm using the properties of logarithms.
- The logarithm of a number between 1 and 10 is the same as the logarithm of that number minus 1.
- So, first, find the logarithm of 1.234 (12.34 minus 1) using the process described above.
- Based on the logarithm table value, the logarithm of 1.234 (to base 10) is approximately 0.0899.
- Lastly, add 1 to the approximate logarithm value: 0.0899 + 1 = 1.0899.
- Therefore, the approximate logarithm of 12.34 (to base 10) is approximately 1.0899.
Please note that the values provided for approximation are rounded for simplicity, and the actual values may have more decimal places in logarithm tables.