Question

How do you evaluate $ \log 100 $ ?

Answer 1

Hint: As we know that the logarithm is the inverse function to exponentiation. That means the logarithm of a given number $ x $ is the exponent to which another fixed number, the base b, must be raised, to produce that number $ x $. As per the definition of a logarithm $ {\log _a}b = c $ which gives that $ {a^c} = b $ . And we also have to assume that if no base $ b $ is written then the base is always 10. This is an example of base-ten logarithms because $ 10 $ is the number that is raised to a power.

Complete step by step answer:
To evaluate $ \log 100 $ we will use the above definition $ {\log _a}b = c \Leftrightarrow {a^c} = b $ and since here no base is given we have to assume that it is $ 10 $ . So in the above given question we have $ {\log _{10}}100 $ which means that $ {10^c} = 100 $ . The base unit is the number being raised to a power.
Now we can easily find that $ c = 2 $ , because ,
 $ {10^2} = 10*10 $ which gives $ 100 $ . Here it can be shown as $ {\log _{10}}100 $ is the question.
 By using the law of logarithms we get that $ c = 2 $ , the variable $ c $ is equal to $ 2 $ .
Hence the answer of $ \log 100 $ is 2 .

Note:
We have to keep in mind that when a logarithm is written without any base, like this: $ \log 100 $ then this usually means that the base is already there which is $ 10 $ . It is called a common logarithm or decadic logarithm, is the logarithm to the base $ 10 $ . One way we can approach log problems is to keep in mind that $ {a^b} = c $ and $ {\log _a}c = b $ .