Question

Using a logarithm table, determine the value of $\log _{10}^{0.5432}$.
(A) $\overline 1 .7350$
(B) $\overline 2 .7350$
(C) $0.7350$
(D) $0.07350$

Answer 1

Hint: We have to find the value of $\log _{10}^{0.5432}$ using logarithm table. By using a logarithm table we have to first calculate the mantissa and characteristics of $0.5432$. And then we have to calculate the sum of characteristics and the mantissa, which is the value of $\log _{10}^{0.5432}$.

Complete step-by-step answer:
Here, we have to determine the value of $\log _{10}^{0.5432}$ using a logarithm table.
Firstly, write $0.5432$ such that one non zero digit is before the decimal point, this imply
$0.5432 = 5.432 \times {10^{ - 1}}$
Now we have to determine the mantissa of $0.5432$.
Mantissa is calculated by seeing the value corresponding to $52$in the row and corresponding to $3$ in the column and then add the value corresponding to $2$ in the mean difference table.
Following above written points we get a mantissa of $0.5432$ is $0.7350$.
Now, find the characteristics of $0.5432$
Characteristics of $0.5432$ can be evaluated by using $\log _{10}^{{{10}^{ - 1}}}$.
Thus, characteristics of $0.5432$ is $ - 1$.
The value of $\log _{10}^{0.5432} = $mantissa $ + $ characteristics
$
   \Rightarrow \log _{10}^{0.5432} = 0.7350 + \left( { - 1} \right) \\
   \Rightarrow \log _{10}^{0.5432} = \overline 1 .7350
 $

Hence, option (A) is the correct answer.

Note: Procedure to find the value $\log _{10}^x$ using logarithm table.
1. write the given number $x$ such that one non zero number comes before the decimal. To convert in this form multiply by ${10^n}$ where n is a suitable number i.e $x = y \times {10^n}$.
2.Take the first two digits of the number $y$ and match the value corresponding to this in the row and third digit in the column and then add this value to the value given corresponding to the fourth digit of the given number $y$ from the mean difference table. This will be the mantissa part.
3. Find a characteristic using formula $\log _{10}^{{{10}^n}} = n$.
4. Add the mantissa and characteristics of the given number $x$ to find the value of $\log _{10}^x$.