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More precisely, let $\\Phi=\\left\\{ \\varphi_{i}\\right\\} _{i\\in\\Lambda}$ be an iterated function system on $I:=[0,1]$ consisting of real analytic contractions, let $p=(p_{i})_{i\\in\\Lambda}$ be a positive probability vector, and let $\\mu$ be the associated self-conformal measure. Suppose that the maps in $\\Phi$ do not have a common fixed point, $0<\\left|\\varphi_{i}'(x)\\right|<1$ for $i\\in\\Lambda$ and $x\\in I$, and $\\Phi$ is exponentially separated. 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