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3^30の桁数をnとすると、10^(n-1)≦3^30<10^n
各辺の常用対数をとると、底10>1なので不等号の向きは変わらず、n-1≦30log₁₀3<n
30log₁₀3=30×0.4771=14.313より、n=15
答え:15桁

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