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Recently by modifying the arguments of Varj\\'u (2019), Rapaport and Varj\\'u (2024) showed that if $t_1,\\ldots, t_m$ are rational numbers and $0<\\lambda<1$, then $$ \\dim \\mu =\\min\\Big \\{ 1, \\; \\frac{\\sum_{j=1}^m p_{j}\\log p_{j}}{ \\log |\\lambda| }\\Big\\}$$ unless $ \\Phi $ has exact overlaps. 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Recently by modifying the arguments of Varj\\'u (2019), Rapaport and Varj\\'u (2024) showed that if $t_1,\\ldots, t_m$ are rational numbers and $0<\\lambda<1$, then $$ \\dim \\mu =\\min\\Big \\{ 1, \\; \\frac{\\sum_{j=1}^m p_{j}\\log p_{j}}{ \\log |\\lambda| }\\Big\\}$$ unless $ \\Phi $ has exact overlaps. 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