Multiplication or division of two large numbers or exponentiation are few tough tasks for kids. Let’s use log and anti-log tables for making your calculations easy.
The basic principle of logarithm is as follows.
Common logarithm (with base 10)
We know that
and
Basic Laws
Remember just one more fact
If 1<x<10, then 0<log x<1
Let us do some problems on multiplication.
1. Multiply 256 and 768
Express each number in the standard form. That is put a decimal after the first digit and multiply by the appropriate power of of 10. The logarithm of a number has two parts the first of which is the exponent of 10, called the characteristic, and the second part is a decimal ,called the mantissa,which is read from the log tables. The characteristic can be positive or negative. The negative characteristic is written with a bar above the number. The mantissa is always a positive decimal less than 1.
To multiply two numbers, find the logarithm of each number and add them. Then find the antilogarithm of the mantissa (the fraction part) from anti-log table (which will be a decimal between 1 and 10) and multiply by 10 raised to the characteristic to get the product.
2. Multiply 67846 and 0.0839
The bar above the characteristic is written to show that only the characteristic part is negative and the mantissa part is positive.
3. Multiply 0.04532 and 0.03487
Now let us do some problems on division.
4. Divide 826 by 347
To divide a number by another number, find their logarithm and subtract the logarithm of the divisor from the logarithm of the dividend. Then find the antilogarithm of the mantissa from anti-log table and multiply by 10 raised to the characteristic to get the result.
5. Divide 273 by 9876
We can find square root of a number using log tables
6. Find the square root of 5468
To find the square root of a number, find its logarithm and divide it by 2 and then find its antilogarithm.
7. Find the square root of 0.8745
Finally let us do the following calculation.
Hope you like this cool method of how to use log tables to multiply or divide two numbers or find the roots of numbers.
