Đặt là a, b nhá
\(a)\) \(7^{x-1}-2.7^{100}=5.7^{100}\)
\(\Leftrightarrow\)\(7^{x-1}=5.7^{100}+2.7^{100}\)
\(\Leftrightarrow\)\(7^{x-1}=7^{100}\left(5+2\right)\)
\(\Leftrightarrow\)\(7^{x-1}=7^{100}.7\)
\(\Leftrightarrow\)\(7^{x-1}=7^{101}\)
\(\Leftrightarrow\)\(x-1=101\)
\(\Leftrightarrow\)\(x=101+1\)
\(\Leftrightarrow\)\(x=102\)
Vậy \(x=102\)
\(b)\) \(5^{x-4}=25\)
\(\Leftrightarrow\)\(5^{x-4}=5^2\)
\(\Leftrightarrow\)\(x-4=2\)
\(\Leftrightarrow\)\(x=2+4\)
\(\Leftrightarrow\)\(x=6\)
Vậy \(x=6\)
Chúc bạn học tốt ~
\(7^{x-1}-2.7^{100}=5.7^{100}\)
\(\Rightarrow7^{x-1}=5.7^{100}+2.7^{100}\)
\(\Rightarrow7^{x-1}=7.7^{100}\)
\(\Rightarrow7^{x-1}=49^{100}\)
\(\Rightarrow7^{x-1}=7^{2^{100}}\)
\(\Rightarrow7^{x-1}=7^{200}\)
\(\Rightarrow x=201\)
Vậy x = 201
\(5^{x-4}=25\)
\(\Rightarrow5^{x-4}=5^2\)
\(\Rightarrow x=6\)
Vậy x = 6
\(\left(2^{100}.5+2^{100}.3\right):2^{101}\)
\(=2^{100}.8:2^{101}\)
\(=2^{100}.2^3:2^{101}\)
\(=2^{103}:2^{101}\)
\(=2^2\)
\(=4\)
\(3^5:3^3+2^2.2^3-14\)
\(=3^2+2^6-14\)
\(=9+64-14\)
\(=59\)
Mình nhầm câu đầu, sorry
Câu a bạn Quân làm đúng nhé
Sorry nhiều
\(7^{x-1}-2.7^{100}=5.7^{100}\)
\(5.7^{100}+2.7^{100}=7^{x-1}\)
\(7^{100}.\left(5+2\right)=7^x:7\)
\(7^{100}.7.7=7^x\)
\(7^{102}=7^x\)
\(\Rightarrow x=102\)
Vậy \(x=102\)
\(5^{x-4}=25\)
\(5^x:5^4=5^2\)
\(5^x=5^2.5^4\)
\(5^6=5^x\)
\(\Rightarrow x=6\)
Vậy \(x=6\)
\(\left(2^{100}.5+2^{100}.3\right):2^{101}=\left[2^{100}.\left(5+3\right)\right]:2^{101}=\left[2^{100}.8\right]:2^{101}=2^{100}.2^3:2^{101}=2^{103}:2^{101}=2^2=4\)
\(3^5:3^3+2^2.2^3-14=3^2+2^5-14=9+32-14=41-14=27\)
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