Question

What is the value of $ \log 16 $ ?

Answer 1

Hint: The word log given in the question is the short form of the word logarithm which means by how much power should we raise the base of the given logarithm to make it equal to the number given in the logarithm, so say for example we have to find the value of $ {\log _2}8 $ it means we have to find the power of the $ 2 $ which will make the number equal to $ 8 $ , and thus it is $ 3 $ , as $ {2^3} = 8 $ .
The question asks us to find the value of $ \log 16 $ . Since no base is given we consider the base to be $ 10 $ . We will solve by using the following formula to solve the question:
 $ \log ({a^b}) = b\log a $
Also remember that value of $ \log 2 $ is given by
 $ \log 2 = 0.301 $ , this is a standard value.

Complete step-by-step answer:
We need to find the value of $ \log 16 $ , we will first express the given logarithm in the terms of $ \log 2 $ . We will do it by using the formula given below,
 $ \log ({a^b}) = b\log a $
As we know that $ 16 = {2^4} $ , the term $ \log 16 $ can be written as,
 $ \Rightarrow \log (16) = \log ({2^4}) $
Solving it using the formula we get,
 $ \Rightarrow \log 16 = 4\log 2 $
The value of $ \log 2 $ is given by
 $ \log 2 = 0.301 $ .
Thus we can write,
 $ \Rightarrow \log 16 = 4 \times 0.301 $
 $ \Rightarrow \log 16 = 1.204 $
Truncating the decimal we can write as,
 $ \log 16 = 1.20 $
Hence this is the final answer to the question.
So, the correct answer is “1.20”.

Note: Remember that when no base is mentioned in the logarithm the bases becomes $ 10 $ , but there is also a logarithm with natural base called as $ \ln $ , which are also type of logs and their base is not $ 10 $ , but a constant called as $ e $ , which is given by,
 $ e = 2.718 $