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Giải bài 1.25 trang 16 sách bài tập toán 7 - Kết nối tri thức với cuộc sống

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) \({5^n}.{\left( {\dfrac{1}{5}} \right)^3} = {5^n}:{5^3}\) b) \(4.3^n = 324\)

Phương pháp giải - Xem chi tiết

a) \({5^n}.{\left( {\dfrac{1}{5}} \right)^3} = {5^n}:{5^3}\) -Thực hiện chia hai luỹ thừa cùng cơ số: giữ nguyên cơ số, trừ hai số mũ. -Biến đổi vế phải thành luỹ thừa với cơ số 5 b) -Thừa số = tích : thừa số đã biết -Biến đổi thành luỹ thừa với cơ số 3 

Lời giải chi tiết

a)\(\begin{array}{l}{5^n}.{\left( {\dfrac{1}{5}} \right)^3} = 125\\ \Rightarrow {5^n}:{5^3} = {5^3}\\ \Rightarrow {5^{n - 3}} = {5^3}\\ \Rightarrow n - 3 = 3\\ \Rightarrow n = 3 + 3\\ \Rightarrow n = 6\end{array}\)Vậy \(n=6\)b)\(\begin{array}{l}{4.3^n} = 324\\ \Rightarrow {3^n} = 324:4\\ \Rightarrow {3^n} = 81\\ \Rightarrow {3^n} = {3^4}\\ \Rightarrow n = 4\end{array}\)Vậy \(n=4\)

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