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a) \(\frac{5}{6}=\frac{x-1}{x}\)
\(5x=6x-6\)
\(6x-5x=6\)
\(x=6\)
các câu còn lại lm tương tự
hok tốt!!
b) \(\frac{1}{2}=\frac{x+1}{3x}\)
\(\Rightarrow1.3x=2.\left(x+1\right)\)
\(3x=2x+2\)
\(3x-2x=2\)
\(x=2\)
Vậy x=2
các câu khác bạn làm tương tự
a) \(3^x=81\)
\(3^x=3^4\)
\(\Rightarrow x=4\)
b) \(2^x.16=128\)
\(2^x=128:16\)
\(2^x=8\)
\(2^x=2^3\)
\(\Rightarrow x=3\)
c) \(3^x:9=27\)
\(3^x=27.9\)
\(3^x=243\)
\(3^x=3^5\)
\(\Rightarrow x=5\)
d) \(x^4=x\)
\(\Rightarrow x=0\)hoac \(\orbr{\begin{cases}x=1\\x=-1\end{cases}}\)
e) \(\left(2x+1\right)^3=27\)
\(\left(2x+1\right)^3=3^3\)
\(\Rightarrow2x+1=3\)
\(\Rightarrow2x=4\)
\(\Rightarrow x=2\)
f) \(\left(x-2\right)^2=\left(x-2\right)^4\)
\(\left(x-2\right)^2-\left(x-2\right)^4=0\)
\(\left(x-2\right)^2-\left(x-2\right)^2.\left(x-2\right)^2=0\)
\(\left(x-2\right)^2\left[1-\left(x-2\right)^2\right]=0\)
\(\left(x-2\right)^2\left(1-x+2\right)\left(1+x-2\right)=0\)
\(\Rightarrow\left(x-2\right)^2=0\)hoac \(\orbr{\begin{cases}3-x=0\\x-1=0\end{cases}}\)
\(\Rightarrow x-2=0\)hoac \(\orbr{\begin{cases}x=3\\x=1\end{cases}}\)
\(\Rightarrow x=2\)hoac \(\orbr{\begin{cases}x=3\\x=1\end{cases}}\)
a) \(3^x=81\Leftrightarrow3^x=3^4\Rightarrow x=4\)
b)\(2^x\times16=128\Leftrightarrow2^x=8\Leftrightarrow2^x=2^3\Rightarrow x=3\)
c) \(3^x\div9=27\Leftrightarrow3^x\div3^2=3^3\Rightarrow x=5\)
d) \(x^4=x\Leftrightarrow x=1\)
e) \(\left(2x+1\right)^3=27\Leftrightarrow\left(2x+1\right)^3=3^3\Rightarrow2x+1=3 \)
\(\Rightarrow2x=3+1\Leftrightarrow2x=4\Rightarrow x=2\)
F)
Bài 1:
\(\text{a) }x.x^2.x^3.x^4.x^5.....x^{49}.x^{50}\)
\(=x^{1+2+3+4+5+...+49+50}\)
\(=x^{\frac{51.50}{2}}\)
\(=x^{1275}\)
\(\text{b) Ta có:}\)
\(4^{15}=\left(2^2\right)^{15}=2^{2.15}=2^{30}\)
\(8^{11}=\left(2^3\right)^{11}=2^{3.11}=2^{33}\)
\(\text{Vì }2^{30}< 2^{33}\text{ nên }4^{15}< 8^{11}\)
Bài 2: Tìm x
\(\left(x-1\right)^4:3^2=3^6\)
\(\Rightarrow\left(x-1\right)^4=3^6\times3^2\)
\(\Rightarrow\left(x-1\right)^4=3^8\)
\(\Rightarrow\left(x-1\right)^4=3^{2.4}\)
\(\Rightarrow\left(x-1\right)^4=\left(3^2\right)^4\)
\(\Rightarrow x-1=9\)
\(\Rightarrow x=10\)
Bài 3 và bài 4 mk làm sau
Bài 1 : a) \(x.x^2.x^3.x^4.....x^{49}.x^{50}=x^{1+2+3+...+49+50}\) (Dễ rồi tự tính)
b) \(\hept{\begin{cases}4^{15}=\left(2^2\right)^{15}=2^{30}\\8^{11}=\left(2^3\right)^{11}=2^{33}\end{cases}}\)Rồi tự so sánh đi
Bài 2 :
\(\left(x-1\right)^4\div3^2=3^6\Leftrightarrow\left(x-1\right)^4=3^8=\left(3^2\right)^4=9^4\Leftrightarrow x-1=9\Leftrightarrow x=10\)
Bài 3 :
\(\hept{\begin{cases}27^{15}=\left(3^3\right)^{15}=3^{45}\\81^{11}=\left(3^4\right)^{11}=3^{44}\end{cases}}\) nt
Bài 1 tự làm!
Bài 2:
a, \(\left(3x-4\right)\left(x-1\right)^3=0\Rightarrow\left[{}\begin{matrix}3x-4=0\\\left(x-1\right)^3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{4}{3}\\x-1=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{4}{3}\\x=1\end{matrix}\right.\)
b, \(2^{2x-1}:4=8^3\Rightarrow2^{2x-1}:2^2=2^9\)
\(\Rightarrow2x-1-2=9\Rightarrow2x-3=9\Rightarrow2x-12\Rightarrow x=6\)
c, Đề chưa rõ
d, \(\left(x+2\right)^5=2^{10}\Rightarrow\left(x+2\right)^5=4^5\Rightarrow x+2=4\Rightarrow x=2\)
e, \(\left(3x-2^4\right).7^3=2.7^4\Rightarrow3x-2^4=2.7^4:7^3\Rightarrow3x-16=2.7=14\)
\(\Rightarrow3x=14+16=30\Rightarrow x=\dfrac{30}{3}=10\)
f, \(\left(x+1\right)^2=\left(x+1\right)^0\Rightarrow\left(x+1\right)^2=1\) (vì x0 = 1)
\(\Rightarrow x+1=1\Rightarrow x=0\)
a) 4x - 15 = - 75 - x
<=> 4x + x = -75 + 15
<=> 5x = -60
<=> x = -12
b) 72 - 3x = 5x + 8
<=> -3x -5x = 8 - 72
<=> -8x = -64
<=> x = 8
d) 3 . | x - 7 | = 21
<=> | x - 7 | = 7
\(\Leftrightarrow\orbr{\begin{cases}x-7=7\\x-7=-7\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=14\\x=0\end{cases}}\)
\(-7\left|x+3\right|=-49\)
\(\Leftrightarrow\left|x+3\right|=7\)
\(\Leftrightarrow\orbr{\begin{cases}x+3=7\\x+3=-7\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=4\\x=-10\end{cases}}\)
a, \(5^x=625\Rightarrow5^x=5^4\Rightarrow x=4\)
b, \(4^{2x-6}=1\Rightarrow4^{2x-6}=4^0\)
\(\Rightarrow2x-6=0\Rightarrow x=3\)
c, \(\left(3x-1\right)^3=8\Rightarrow3x-1=2\)
\(\Rightarrow x=1\)
d, \(49.7^n=2401\Rightarrow7^{n+2}=7^4\)
\(\Rightarrow n+2=4\Rightarrow n=2\)
e, \(x^4.x-27.x=0\)
\(\Rightarrow x\left(x^4-27\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x^4-27=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=0\\x=\pm\sqrt[4]{27}\end{cases}}\)
f, \(\left(x-6\right)^3=\left(x-6\right)^2\)
\(\Rightarrow\left(x-6\right)^3-\left(x-6\right)^2=0\)
\(\Rightarrow\left(x-6\right)^2\left(x-6-1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-6=0\\x-7=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=6\\x=7\end{cases}}\)
Chúc bạn học tốt!!!
\(a,5^x=625\) \(b,4^{2x-6}=1\)
\(\Rightarrow5^x=5^4\) \(\Rightarrow2x-6=0\) (Vì mọi số mũ không bằng 1)
\(\Rightarrow x=4\) \(\Rightarrow2x=6\)
\(\Rightarrow x=3\)
\(c,\left(3x-1\right)^3=8\) \(d,49.7^n=2401\)
\(\Rightarrow\left(3x-1\right)^3=2^3\) \(\Rightarrow7^n=2401:49\)
\(\Rightarrow3x-1=2\) \(\Rightarrow7^n=49\)
\(\Rightarrow3x=3\) \(\Rightarrow7^n=7^2\)
\(\Rightarrow x=1\) \(\Rightarrow n=2\)
\(e,x^4.x-27.x=0\)
\(\Rightarrow x.\left(x^4-27\right)=0\)
\(\Rightarrow\hept{\begin{cases}x=0\\x^4-27=0\end{cases}\Rightarrow\hept{\begin{cases}x=0\\x^4=27\end{cases}}}\)
\(f,\left(x-6\right)^3=\left(x-6\right)^2\)
\(\Rightarrow x.\left(x^4-27\right)=0\) \(\Rightarrow\hept{\begin{cases}\left(x-6\right)^3=\left(x-6\right)^2\\\left(x-6\right)^3=\left(x-6\right)^2\end{cases}\Rightarrow\hept{\begin{cases}\left(x-6\right)^3:\left(x-6\right)^2=1\\\left(x-6\right)^3-\left(x-6\right)^2=0\end{cases}\Rightarrow}\hept{\begin{cases}x-6=1\\x-6=0\end{cases}}\Rightarrow\hept{\begin{cases}x=7\\x=6\end{cases}}}\)