Question

what is the value of log 100 base 1? explain it ​

Answer 1

$what \: is \: log_{1}(100) .$

Before your question,

Consider this :

$what \: is \: log_{a}(b)$

Let log of b to the base a equals k.

Since log of something(b) is nothing but the exponent(k) to which the base(a) must be raised to obtain the number (b).

$= > log_{a}(b) = k \\= > {a}^{k} = b$

Now consider this,

$log_{1}(100) = k \\ = > {1}^{k} = 100$

Hence, there is no number to which

when 1 is raised, will give 100.

So, Logarithmic never take a = 1 or a < 0 in bases or else the expression will become invalid.

Therefore, Log 100 to the base 1 is Meaningless or undefined.

Hope this helps !