A differentiable function satisfy the relation \( \ln (f(x+y))=\ln (f(x)) . \ln (f(y)) \forall x....

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A differentiable function satisfy the relation \( \ln (f(x+y))=\ln (f(x)) . \ln (f(y)) \forall x, y \in R, f(0) \neq 1 \),
P
\( f^{\prime}(0)=\mathrm{e} \) and \( g \) be the inverse of \( f \).

The number of solutions of the equation \( \ln [\ln f(x)]=g^{2}[f(x)]-3 g[f(x)]-5 \) is(are) :
(1) 0
(2) 1
(3) 2
(4) Infinite


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