Question

How do you expand $\log (5.3)$?

Answer 1

Hint: We are given a log number and we have to expand it. As it is of the form. So we will use the law of log to find its solution.
Log(a.b)=loga+logb
Here we have used the law of multiplication inside the log that can be turned into addition outside the log and vice-versa. Then from the log table we will substitute the value of the logs and then add the values to get the result.

Complete step-by-step solution:
Step1: We are given a log(5.3) as it is the multiplication of log. So we will use the law of multiplication of log that can be turned into addition outside the log by using the formula.
Log(a.b)=loga+logb
Here a=5, b=3. On substituting the value in the formula we will get
$ \Rightarrow \log (5.3) = \log 5 + \log 3$
Step2: Now from the log table we will put the value of $\log 5$,$\log 3$
$\log 5 = 0.6989$;$\log 3 = 0.4771$
$ \Rightarrow \log (5.3) = 0.6989 + 0.4771$
$ = 1.176$

The value for the given logarithm is 1.176.

Note: The rule when we multiply two values with the same base together $({x^2} \times {x^3})$ in this we keep the base and add the exponents. Well, remember that logarithms are exponents, and when you multiply, you’re going to add the logarithms. The log of a product is the sum of the logs.
These types of questions are mainly solved by the laws of logs and the base of log is mainly considered as 10. If it has any other ways than it is mentioned. Student should learn important value like log2, log3, log5. Student should apply the law correctly in this we have used a multiplication law there are other laws are also like law of exponents all of division which can be used and applied depending on the question.