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15 tháng 12 2019
(-3/4)63x-1=(3/4)^3
3x-1=3+1
3x=3=1
x=4;3
x=4/3
Vậy x=4/3
29 tháng 12 2018
\(64^x.16^x=256^{12}:1024\)
\(\Rightarrow\) \(\left(4^3\right)^x.\left(4^2\right)^x=\left(4^4\right)^{12}:4^5\)
\(\Rightarrow\) \(4^{3x}.4^{2x}=4^{48}:4^5\)
\(\Rightarrow\) \(4^{3x+2x}=4^{43}\)
\(\Rightarrow\) \(3x+2x=43\)
\(\Rightarrow\) \(\left(3+2\right)x=43\)
\(\Rightarrow\) \(5x=43\)
\(\Rightarrow\) \(x=\frac{43}{5}\)
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
20 tháng 7 2023
64\(^x\) : 16\(^x\) = 256
(64: 16)\(x\) = 256
4\(^x\) = 44
\(x\) = 4
Vậy \(x\) = 4
22 tháng 9 2019
Bài 1:
a.
Ta có tỉ lệ thức: 4,5 x 14,4 = 6 x 10,8
\(\Rightarrow\frac{4,5}{6}=\frac{10,8}{14,4};\frac{4,5}{10,8}=\frac{6}{14,4};\frac{6}{4,5}=\frac{14,4}{10,8};\frac{10,8}{4,5}=\frac{14,4}{6}\)
b.
Ta có tỉ lệ thức 1: 4 x 1024 = 16 x 256
\(\Rightarrow\frac{4}{16}=\frac{256}{1024};\frac{4}{256}=\frac{16}{1024};\frac{16}{4}=\frac{1024}{256};\frac{256}{4}=\frac{1024}{16}\)
Ta có tỉ lệ thức 2: 16 x 64 = 4 x 256
\(\Rightarrow\frac{16}{4}=\frac{256}{64};\frac{16}{256}=\frac{4}{64};\frac{4}{16}=\frac{64}{256};\frac{256}{16}=\frac{64}{4}\)
Bài 2:
Áp dụng t/c DTSBN. ta có:
\(\frac{x}{11}=\frac{y}{7}=\frac{x+y}{11+7}=\frac{-54}{18}=-3\)
\(\Rightarrow x=11.\left(-3\right)=-33\)
\(\Rightarrow y=7.\left(-3\right)=-21\)
LG
1
17 tháng 1 2020
\( {64^{x - 1}}:{4^{x + 1}} = {\left( {{{256}^x}} \right)^2}\\ \Leftrightarrow {4^{3x - 3}}:{4^{x + 1}} = {256^{2x}}\\ \Leftrightarrow {4^{2x - 4}} = {4^{8x}}\\ \Leftrightarrow 2x - 4 = 8x\\ \Leftrightarrow - 6x = 4\\ \Leftrightarrow x = - \dfrac{2}{3} \)
LD
1 tháng 1 2018
Sửa đề
\(\dfrac{\dfrac{1}{3}-\dfrac{1}{7}-\dfrac{1}{13}}{\dfrac{2}{3}-\dfrac{2}{7}-\dfrac{2}{13}}\cdot\dfrac{\dfrac{3}{4}-\dfrac{3}{16}-\dfrac{3}{64}-\dfrac{3}{256}}{\dfrac{1}{4}-\dfrac{1}{6}-\dfrac{1}{64}-\dfrac{1}{256}}+\dfrac{5}{8}\)
\(=\dfrac{\dfrac{1}{3}-\dfrac{1}{7}-\dfrac{1}{13}}{2\left(\dfrac{1}{3}-\dfrac{1}{7}-\dfrac{1}{13}\right)}\cdot\dfrac{3\left(\dfrac{1}{4}-\dfrac{1}{6}-\dfrac{1}{64}-\dfrac{1}{256}\right)}{\dfrac{1}{4}-\dfrac{1}{6}-\dfrac{1}{64}-\dfrac{1}{256}}+\dfrac{5}{8}\)
\(=\dfrac{1}{2}\cdot3+\dfrac{5}{8}=\dfrac{3}{2}+\dfrac{5}{8}=\dfrac{17}{8}\)
AN
1 tháng 1 2018
A= \(\dfrac{\dfrac{1}{3}-\dfrac{1}{7}-\dfrac{1}{13}}{\dfrac{2}{3}-\dfrac{2}{7}-\dfrac{2}{13}}.\dfrac{\dfrac{3}{4}-\dfrac{3}{16}-\dfrac{3}{64}-\dfrac{3}{256}}{1-\dfrac{1}{4}-\dfrac{1}{16}-\dfrac{1}{64}}+\dfrac{5}{8}\)
=> \(\dfrac{\dfrac{1}{3}-\dfrac{1}{7}-\dfrac{1}{13}}{2.(\dfrac{1}{3}-\dfrac{1}{7}-\dfrac{1}{13})}.\dfrac{3.(\dfrac{1}{4}-\dfrac{1}{16}-\dfrac{1}{64}-\dfrac{1}{256})}{\dfrac{4}{4}-\dfrac{1}{4}-\dfrac{1}{16}-\dfrac{1}{64}}+\dfrac{5}{8}\)
=> \(\dfrac{\dfrac{1}{3}-\dfrac{1}{7}-\dfrac{1}{13}}{2.(\dfrac{1}{3}-\dfrac{1}{7}-\dfrac{1}{13})}.\dfrac{3.(\dfrac{1}{4}-\dfrac{1}{16}-\dfrac{1}{64}-\dfrac{1}{256})}{4.(\dfrac{1}{4})-\dfrac{1}{4}-\dfrac{1}{16}-\dfrac{1}{64}}+\dfrac{5}{8}\)
=> \(\dfrac{1}{2}.\dfrac{3.(\dfrac{1}{4}-\dfrac{1}{16}-\dfrac{1}{4^3}-\dfrac{1}{16^2})}{4.(\dfrac{1}{4})-\dfrac{1}{4}-\dfrac{1}{16}-\dfrac{1}{64}}+\dfrac{5}{8}\)
=> \(\dfrac{1}{2}.\dfrac{3.(-\dfrac{1}{4^2}-\dfrac{1}{16^2})}{4-\dfrac{1}{4^3}}+\dfrac{5}{8}\)
=> \(\dfrac{1}{2}.\dfrac{3.(-\dfrac{1}{16^2})}{4.-\dfrac{1}{4^2}}+\dfrac{5}{8}\)
a) \(64^x:16^x=256\)
\(\Rightarrow\left(2^6\right)^x:\left(2^4\right)^x=2^8\)
\(\Rightarrow2^{6x}:2^{4x}=2^8\)
\(\Rightarrow2^{6x-4x}=2^8\)
\(\Rightarrow2^{2x}=2^8\)
\(\Rightarrow2x=8\)
\(\Rightarrow x=4\)
b) \(\dfrac{-2401}{7^x}=-7\)
\(\Rightarrow\dfrac{-7^4}{7^x}=-7\)
\(\Rightarrow-7^{4-x}=-7\)
\(\Rightarrow7^{4-x}=7\)
\(\Rightarrow4-x=1\)
\(\Rightarrow x=4-1\)
\(\Rightarrow x=3\)
c) \(\dfrac{64}{\left(-4\right)^x}=-256\)
\(\Rightarrow\left(-4\right)^x=\dfrac{64}{-256}\)
\(\Rightarrow\left(-4\right)^x=-4\)
\(\Rightarrow\left(-4\right)^x=\left(-4\right)^1\)
\(\Rightarrow x=1\)
\(a) 64^x:16^x=256\\\Rightarrow (64:16)^x=256\\\Rightarrow 4^x=4^4\\\Rightarrow x=4\\---\)
\(b,\dfrac{-2401}{7^x}=-7\)
\(\Rightarrow7^x=-2401:\left(-7\right)\)
\(\Rightarrow7^x=343\)
\(\Rightarrow7^x=7^3\)
\(\Rightarrow x=3\)
\(c,\dfrac{64}{\left(-4\right)^x}=-256\)
\(\Rightarrow\left(-4\right)^x=64:\left(-256\right)\)
\(\Rightarrow\left(-4\right)^x=-\dfrac{1}{4}\)
\(\Rightarrow\left(-4\right)^x=\left(-4\right)^{-1}\)
\(\Rightarrow x=-1\)
#\(Toru\)