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Bài 13 trang 35 SGK Toán 11 tập 2 - Chân trời sáng tạo

Biết rằng \({5^x} = 3\) và \({3^y} = 5\).

💧Tổng hợp đề thi học kì 2 lớp 11 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Lí - Hóa - Sinh
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Đề bài

Biết rằng \({5^x} = 3\) và \({3^y} = 5\). Không sử dụng máy tính cầm tay, tính giá trị của \(xy\).

Phương pháp giải - Xem chi tiết

Sử dụng định nghĩa lôgarit, tìm \(x,y\) sau đó sử dụng công thức đổi cơ số để tính \(xy\).

Lời giải chi tiết

\(\begin{array}{l}{5^x} = 3 \Leftrightarrow x = {\log _5}3;{3^y} = 5 \Leftrightarrow y = {\log _3}5\\ \Rightarrow xy = {\log _5}3.{\log _3}5 = {\log _5}3.\frac{1}{{{{\log }_5}3}} = 1\end{array}\)

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