Question

How do we calculate $\log (1024)$ ?

Answer 1

Hint : According to the question, to find the value of a given logarithmic term, we should go through the logarithm rules. This question will be solved by the help of Power Rule. In power rule, exponent replaced in front of the log as a multiplication of it.

Complete step-by-step answer :
First write the given logarithmic term:
$\log (1024)$
Most of the time, we have to try that our logarithmic base should be 2. So, we have to see here that 1024 is how many times of 2 whether or not. If we multiplied 2 by ten times then we will get 1024. Or, we can also write as ${2^{10}}$ ( 10 is an exponent on the base 2).
So, we can write $\log (1024)$ as $\log ({2^{10}})$ .
Now, according to the Logarithm Law or rules:
$\because \log ({x^{a}}) =a\log (x)$ , this is the power rule of Logarithm. The logarithm of an exponential number is the exponent times the logarithm of the base.
So, according to the Power Rule, now we can write as:
$10.\log 2$
As we know the logarithmic value table, the value of $\log 2$ is almost equal to $0.30103$ , which is a very good approximation.
Now, we have to put the value of $\log 2$ in the term $10.\log 2$ . So, we get:
$10.\log 2 = 10 \times 0.30103 \approx 3.0103$
So, the value of $10.\log 2$ is almost approximately 3.0103.
So, the correct answer is “approximately 3.0103”.

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