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How do you evaluate log164?

Answer
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Hint:In order to solve this question, firstly we have to understand what logarithm of a number means. If the written logarithm of a in base b equals c, then it means a is equal to c raised to the power of b. Understanding this mathematically as follows
logba=cbc=a
Use this information to evaluate the given logarithm.

Complete step by step answer:
In order to evaluate log164, let us understand first what logarithm means in a general way and the function of a logarithmic function.Consider a logarithm of a with base b equal to c, it means that when c is raised to the power of b then it will equal to a, let’s understand this in mathematical way or in equations
logba=c
It is the mathematical form of the first part of the consideration. Now coming to second part
bc=a(i)
It is the mathematical form of the second part.
Hope that you got to understand the logarithmic function.

Now let’s come to the question, that is log164 or logarithm of 4 with base 16.Let us consider log164 equals to x, then it will be written in mathematical equation as follows,
log164=x
Now writing this equation as equation (i) is written, we get
16x=4
Solving this further, by converting 16 into multiples of 2,
(2×2×2×2)x=2×224x=22
Now comparing the power of both sides, because their bases are same i.e. 2 we get,
4x=2x=24x=12
We got the value of xthat means,
log164=12

Note:Logarithm has some strict rules with it, that is the base of logarithm should be greater than 0 and should not be equal to 1, also logarithmic functions never take negative arguments. These limits are sometimes used to solve logarithmic problems.