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Reference: Wikipedia:
"An expression is said to be referentially transparent if it can be replaced with its value without changing the behavior of a program (in other words, yielding a program that has the same effects and output on the same input). The opposite term is referentially opaque."

So log(x) is referentially transparent, rest are referentially opaque.

Because for given x, log(x) has a certain value. But in case of:
now(): time changes so you can't possibly replace it with an exact value.
strcat(str1, gets()): result depends upon input string received from gets.
rand(0, 1): random number between 0 and 1, cannot have certain value, it will be different each time it is called.

log(x) as it can be replaced by a definite answer, others cannot be...

Its rand(0,1)..Since it will only output 1 or 0 and we will get to know the answer..but in other cases you will have to depend on other things.