Question

The antilog of (4.8779) will be
A. 7500
B. 750
C. 75500
D. 750000

Answer 1

Hint: We know that the antilog of a number is equal to raising 10 to the power of the number, so the antilog of $x={{10}^{x}}$. Also, we will use the value of ${{10}^{-0.1221}}$ equals 0.755 approximately. In this way we can get the required antilog.

Complete step-by-step answer:
We have been asked to find the antilog of (4.8779). To solve the question, let us take,
${{\log }_{10}}x=4.8779$
On taking antilog on both the sides, we get,
${{10}^{{{\log }_{10}}x}}={{10}^{4.8779}}$
We know that the property of a logarithm function, which states that ${a}^{{\log }_{a}}x$ is equal to x. So, we can write the above as,
$x={{10}^{4.8779}}$
We know that ${{x}^{a}}\times {{x}^{b}}={{x}^{a+b}}$. So, using this relation, we will break the powers in the above equality. So, we will get,
$x={{10}^{5}}\times {{10}^{-0.1221}}$
Now, we know that ${{10}^{-0.1221}}$ is approximately equal to 0.755. So, we will use that value in the above equality. So, we will get,
$\begin{align}
  & x={{10}^{5}}\times 0.755 \\
 & \Rightarrow x=75500 \\
\end{align}$
Hence, we have obtained the value of the antilog of (4.8779) as 75500.
Therefore, the correct answer is option C.

Note: We can also write the term ${{10}^{4.8779}}$ as ${{10}^{4}}\times {{10}^{0.8779}}$. Then we know that the approximate value of ${{10}^{0.8779}}$ is 7.55, so we will get the answer as ${{10}^{4}}\times 7.55=75500$. We can also use another method by using the antilog table to find the antilog for the given number. We should remember that the approximate value of logarithm to base 10, like log 1, log 2, log 3, log 7, so that you can choose the correct answer quickly in examinations, which will let you save time and it would be beneficial from the competitive examination point of view.