Question

How do you evaluate \[\log 12 - \log 3\] ?

Answer 1

Hint: In the above question, we are given a difference of two functions and we have to find their value, the given functions are logarithmic functions. So to solve this question, we must know what logarithm functions are. A logarithm function is the inverse of an exponential function (a function in which one term is raised to the power of another term is known as an exponential function). An exponential function is of the form $ a = {x^y} $ , so the logarithm function being the inverse of the exponential function is of the form $ y = {\log _x}a $ . To evaluate this question, we will use the laws of the logarithm.

Complete step-by-step answer:
The standard base of logarithm functions is 10, that is, if we are given a function without any base like $ \log x $ then we take the base as 10, so the base of both $ \log 12 $ and $ \log 3 $ is 10. Now while applying the laws of the logarithm, we should keep in mind an important rule that is the base of the logarithm functions involved should be the same in all the calculations, as the base of both the functions in the question is the same, we can apply the logarithm laws in the given question.
We have to evaluate
$ \log 12 - \log 3 $
We know that
 $
  \log x - \log y = \log \dfrac{x}{y} \\
   \Rightarrow \log 12 - \log 3 = \log \dfrac{{12}}{3} = \log 4 \\
  $
Now $ \log 4 = 0.602059991 $
Hence, the value of $ \log 12 - \log 3 $ is $ 0.602 $ .
So, the correct answer is “ $ 0.602 $ ”.

Note: There are several laws of the logarithm that make the calculations easier and help us evaluate the logarithm functions. The three laws of the logarithm include one of addition, one of subtraction and the other to convert logarithm functions to exponential functions. In the given question, the two logarithm functions are in subtraction with each other so we have used the law for subtraction