Why is y loga1always equal to 0 for any valid base a Explai

Solution

Well, by defninition 10 to the power of 0 is equal to 1, so that is why the Log(1) =0!

In fact, since any number - except 0 - raised to the power of 0 gives 1, then the logarithm of the value of 1 will always be zero no matter what base you are working in.

First i would like to mention the relation between logarithms and exponents.
If a number \'a\' is multiplied with itself \'n\' number of times, we write it as a^n.
Let us assign it to another variable \'b\'. Here \'b\' is the exponential notation of the product obtained when \'a\' is multiplied with itself \'n\' times.
If we convert this ( b= a^n) into logarithmic form, we can write it as n= log b base a.
now on applying the same concept to log 1, log 1 base 10 can be written as 10^0 which is equal to 1 ( as any number raised to the power 0 is equal to 1).