Question

$log_{100}10 =$
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Answer 1

It is $\rm{{log}_{100}} 10 = \dfrac{1}{2}$.

Why? Let assume that,

$\rm{{log}_{100}} 10 = x$.

∴ In radical form,

$100^x = 10$

⇒ $10^{2x} = 10^1$

∴ As bases are equal,

$2x = 1 \implies x = \dfrac{1}{2}$.

More:-

Laws of logarithm and constraints of it.

(See attachment.)