AMC 12B 2025 (Problem 24)How many real numbers satisfy the equation sin(20πx)=log20(x)\sin(20\pi x)=\log_{20}(x)sin(20πx)=log20(x)?(A) 199\text{(A)}\;199(A)199(B) 200\text{(B)}\;200(B)200(C) 398\text{(C)}\;398(C)398(D) 399\text{(D)}\;399(D)399(E) 400\text{(E)}\;400(E)400Related TopicsCoreToolkit 121 — Trigonometric Functions GraphsMajorToolkit 48 — Logarithms: Definition and PropertiesHints (2)Hint 1Hint 2log20(x)=−1⇒x=20−1=120\log_{20}(x)=-1\Rightarrow x=20^{-1}=\frac{1}{20}log20(x)=−1⇒x=20−1=201log20(x)=1⇒x=20\log_{20}(x)=1\Rightarrow x=20log20(x)=1⇒x=20Ans=399\text{Ans}=399Ans=399Final Answer(D) 399399399Related Problems (9)AMC 12B 2025 (Problem 7)AMC 12B 2024 (Problem 8)AMC 12A 2024 (Problem 8)AMC 12A 2022 (Problem 14)AMC 12A 2023 (Problem 19)AMC 12A 2025 (Problem 7)AIME I 2026 (Problem 6)AMC 12B 2024 (Problem 15)View all related problems →
