Answer:
False.
Step-by-step explanation:
Data provided in the question:
f(x) = In x
To check: [tex](f(x))^{\frac{1}{2}} = \frac{1}{2}\times\ f(x)[/tex]
now,
substituting the function in the given relation
[tex](\ln(x))^{\frac{1}{2}} = \frac{1}{2}\times\ln(x)[/tex]
also, we know
log(aᵇ) = b × log(a)
therefore,
[tex](\ln(x))^{\frac{1}{2}}[/tex] ≠ [tex]\ln(x^{\frac{1}{2}})[/tex]
here,
LHS is not equal to RHS
Hence,
The given relation in the question is False.
