Question

How do I find the value of $\log 1000$?

Answer 1

Hint:
In this particular sum the student should assume the base of the given logarithm to be $10$. Since it is not mentioned in the question , the student can choose on its own. We have taken this assumption as we know one of the properties of logarithmic functions i.e. ${\log _a}a = 1$. Another property which we are going to use in this sum is $\log {a^b} = b\log a$. Combining these two properties we will solve the entire problem.

Complete step by step solution:
First step is to assume the base for the given numerical. In order to make the problem simpler we are going to assume the base as $10$.
The given sum can now be written as ${\log _{10}}1000$.
Also we know that $10$is the cube root of $1000$. Using this in the next step we get
${\log _{10}}1000 = {\log _{10}}{10^3}........(1)$
We can now use the property of logarithm i.e. $\log {a^b} = b\log a$
${\log _{10}}1000 = 3{\log _{10}}10........(2)$
Also, from another property of logarithm we know that ${\log _a}a = 1$
Thus we can say that , \[{\log _{10}}1000 = 3 \times 1\]

Answer is \[3\].

Note:
As we have seen from the above numerical, the properties of logarithm play a very important role while solving the sum. The student should be well acquainted with all the properties as they make the problem much simpler. Students should always use logarithm whenever algebraic equations are involved to solve a particular sum, for example $256 = {2^{{x^2}}}$. IN this sum students can use the properties of logarithm instead of using the identities of indices. Logarithmic methods are the safest methods which have negligible chance of going wrong if done properly.