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Giải bài 5 trang 21 vở thực hành Toán 7

Tìm số tự nhiên\(n\), biết:

🔯Tổng hợp đề thi học kì 2 lớp 7 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Khoa học tự nhiên...
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Đề bài

Tìm số tự nhiên\(n\), biết: a, \({5^n}.4 = 100;\) b,\({3^n}.{\left( {\frac{1}{9}} \right)^4} = 27.\)

Phương pháp giải - Xem chi tiết

-       Áp dụng quy tắc chuyển vế đổi dấu đế đưa 1 vế về số hạng chỉ chứa n, 1 vế là số hạng tự do -       Tính lũy thừa của 1 số để tìm n.

Lời giải chi tiết

\(\begin{array}{l}{5^n}.4 = 100\\ \Leftrightarrow {5^n} = 100:4\\ \Leftrightarrow {5^n} = 25\\ \Leftrightarrow {5^n} = {5^2}\\ \Leftrightarrow n = 2\end{array}\)Vậy \(n = 2.\)b,\(\begin{array}{l}{3^n}.{\left( {\frac{1}{9}} \right)^4} = 27\\ \Leftrightarrow {3^n} = {3^3}:{\left( {\frac{1}{{{3^2}}}} \right)^4} = {3^3}:{\left( {\frac{1}{3}} \right)^8}\\ \Leftrightarrow {3^n} = {3^3}{.3^8}\\ \Leftrightarrow {3^n} = {3^{11}}\\ \Leftrightarrow n = 11\end{array}\)Vậy\(n = 11.\)

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