Using log tables evaluate 0.6283×17.85
Wow, you still have log tables?
if you insist, but I will use my calculator and round the results to 4 decimals
since most of the log tables they had in the 60s and 70s had only 4 decimals
let x = 0.6283×17.85
log x = log(0.6283×17.85)
= log 0.6283 + log 17.85
= (-1 + .7982) + (1 + .2516) , I remembered all that mantissa stuff
= -.2018 + 1.2516
log x = 1.0498
x = 10^1.0498
I suppose you also had antilog tables
x = 10^1.0498
= 10^1 * 10^.0498 , find .0498 in the anti-log tables
= 10 * 1.12150
= 11.2150
To evaluate the expression 0.6283 × 17.85 using log tables, we can follow these steps:
Step 1: Take the logarithm of both numbers.
- Log(0.6283) = -0.2016
- Log(17.85) = 1.2510
Step 2: Add the logarithms to get:
- (-0.2016) + 1.2510 = 1.0494
Step 3: Use the anti-logarithm table to find the value of 1.0494.
- The anti-log(1.0494) = 10^1.0494 = 11.266
Therefore, 0.6283 × 17.85 equals approximately 11.266 when using log tables.
To evaluate the expression 0.6283 × 17.85 using log tables, we can express it in the form of a logarithm equation.
First, take the natural logarithm (ln) of both sides:
ln(0.6283 × 17.85) = ln(x)
Using the logarithmic property, we can simplify this expression by splitting the product into the sum of logarithms:
ln(0.6283) + ln(17.85) = ln(x)
Next, we need to find the logarithmic values of 0.6283 and 17.85 in the log table.
The log table provides the logarithms of values in the range 1 to 10. Since 0.6283 is smaller than 1, we need to convert it to a number between 1 and 10. We can do this by moving the decimal point to the right until the number is greater than or equal to 1. In this case, moving the decimal point 3 places to the right gives us 6.283.
Now, we find the logarithm of 6.283 in the log table, which is 0.7971.
Similarly, we find the logarithm of 17.85, which is 1.2500 in the log table.
Now, we substitute these values back into the logarithmic equation:
ln(0.6283) + ln(17.85) = 0.7971 + 1.2500
Add these values together:
0.7971 + 1.2500 = 2.0471
Therefore, the natural logarithm of 0.6283 × 17.85 is approximately 2.0471.
Please note that in order to calculate the final result, you would need to use the antilog table to find the value corresponding to 2.0471. The antilog table provides the values for raising 10 to a given power. In this case, you would need to find the value corresponding to 2.0471 and multiply it by the correct scale factor (0.6283 × 17.85) to obtain the final result.