
The mantissa of is .8821259; write down the logarithms of 7.623, 762.3, .007623, 762300, .000007623.
Answer
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Hint: Here, we need to solve the logarithm of decimal numbers. We can use the formula:
characteristics + mantissa
Complete step-by-step answer:
We will find the characteristics first and then use the mantissa value given in the question.
Take 7.623,
Taking logarithm on both sides, (using the rule of sandwich theorem)
We found that the characteristic of log 7.623 is 0
So from sandwich theorem it is clear that the value of log 7.623 lies in between 0 and 1.
From the given information we know that mantissa of log 623 is 0.8821259 (or we can use log table)
Then the value of log 7.623 = characteristic + mantissa
7.623 = 0 + .8821259 = 0.8821259.
Here we use the value of log 7.623 to find remaining values or we can repeat the above procedure.
= 2 + 0.8821259 = 2.8821259
= 0.8821259 – 3 = -2.1178741
= 5 + 0.8821259 = 5.8821259
= 0.8821259 - 6 = -5.1178741
Note: Integer portion of the value of a logarithm is called characteristic and the fractional part (part of number which is located after decimal point) is called mantissa. For example log 27=1.431, here 1 is the characteristic and 0.431 is mantissa. To find the logarithmic value of a decimal number (ex.762.3) we have to find the characteristic and mantissa. Then adding both of them will give the value of a decimal number.
Complete step-by-step answer:
We will find the characteristics first and then use the mantissa value given in the question.
Take 7.623,
Taking logarithm on both sides, (using the rule of sandwich theorem)
We found that the characteristic of log 7.623 is 0
So from sandwich theorem it is clear that the value of log 7.623 lies in between 0 and 1.
From the given information we know that mantissa of log 623 is 0.8821259 (or we can use log table)
Then the value of log 7.623 = characteristic + mantissa
Here we use the value of log 7.623 to find remaining values or we can repeat the above procedure.
Note: Integer portion of the value of a logarithm is called characteristic and the fractional part (part of number which is located after decimal point) is called mantissa. For example log 27=1.431, here 1 is the characteristic and 0.431 is mantissa. To find the logarithmic value of a decimal number (ex.762.3) we have to find the characteristic and mantissa. Then adding both of them will give the value of a decimal number.
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