Answer
No.
The principle can not be applied to functions that are not one-to-one, such as $f(x)=x^{2}.$
Work Step by Step
The principle of logarithmic equality is a direct consequence of the logarithmic function being one-to-one.
(different inputs have different outputs,
so, if the outputs are equal, then so must be the inputs).
To answer the question, no.
The principle can not be applied to functions that are not one-to-one.
Example: $f(x)=x^{2}.$
$f(-1)=f(1)$, but $-1\neq 1.$
Note:
The principle CAN be generalized to one-to-one functions
(but not to all functions)
