tính
a) \(log_2\dfrac{1}{16}\)
b) \(log_3243\)
c) \(9^{log_37}\)
d) \(\left(\dfrac{1}{81}\right)^{log_32}\)
K
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Những câu hỏi liên quan
HQ
Hà Quang Minh
Giáo viên
26 tháng 8 2023
\(a,\left(\dfrac{1}{9}\right)^{x+1}>\dfrac{1}{81}\\ \Leftrightarrow\left(\dfrac{1}{9}\right)^{x+1}>\left(\dfrac{1}{9}\right)^2\\ \Leftrightarrow x+1< 2\\ \Leftrightarrow x< 1\)
\(b,\left(\sqrt[4]{3}\right)^x\le27\cdot3^x\\ \Leftrightarrow3^{\dfrac{x}{4}}\le3^{x+3}\\ \Leftrightarrow\dfrac{x}{4}\le3=x\\ \Leftrightarrow-\dfrac{3}{4}x\le3\\ \Leftrightarrow x\ge-4\)
c, ĐK: \(\left\{{}\begin{matrix}x+1>0\\2-4x>0\end{matrix}\right.\Leftrightarrow-1< x< \dfrac{1}{2}\)
\(log_2\left(x+1\right)\le log_2\left(2-4x\right)\\ \Leftrightarrow x+1\le2-4x\\ \Leftrightarrow5x\le1\\ \Leftrightarrow x\le\dfrac{1}{5}\)
Kết hợp với ĐKXĐ, ta được: \(-1< x\le\dfrac{1}{5}\)
17 tháng 6 2023
1:
a: =7/5(40+1/4-25-1/4)-1/2021
=21-1/2021=42440/2021
b: =5/9*9-1*16/25=5-16/25=109/25
22 tháng 7 2021
a) Ta có: \(\dfrac{5}{8}+\dfrac{3}{17}+\dfrac{4}{18}+\dfrac{20}{-17}+\dfrac{-2}{9}+\dfrac{21}{56}\)
\(=\left(\dfrac{3}{17}-\dfrac{20}{17}\right)+\left(\dfrac{2}{9}-\dfrac{2}{9}\right)+\left(\dfrac{5}{8}+\dfrac{3}{8}\right)\)
\(=-1+1=0\)
b) Ta có: \(\left(\dfrac{9}{16}+\dfrac{8}{-27}\right)+\left(1+\dfrac{7}{16}+\dfrac{-19}{27}\right)\)
\(=\left(\dfrac{9}{16}+\dfrac{7}{16}\right)+\left(\dfrac{-8}{27}-\dfrac{19}{27}\right)+1\)
=1-1+1=1
21 tháng 4 2022
a. 7/9 - 16/9 = -9/9 = -1
b. 2/-15 + 7/10 = 17/30
c. (4 2/3 - 4 3/4) : -5/12 - 4/5
= (14/3 - 19/4) : (-5/12) - 4/5
= -1/12 : (-5/12) - 4/5
= 1/5 - 4/5
= -3/5
NV
Nguyễn Việt Lâm
Giáo viên
12 tháng 1
ĐKXĐ:
a.
\(2x-4>0\Rightarrow x>2\Rightarrow D=\left(2;+\infty\right)\)
b.
\(2x+8>0\Rightarrow x>-4\Rightarrow D=\left(-4;+\infty\right)\)
c.
\(4-x>0\Rightarrow x< 4\Rightarrow D=\left(-\infty;4\right)\)
d.
\(\dfrac{1}{x+4}>0\Rightarrow x>-4\Rightarrow D=\left(-4;+\infty\right)\)
e.
\(\left(x-3\right)\left(x+9\right)>0\Rightarrow\left[{}\begin{matrix}x>3\\x< -9\end{matrix}\right.\) \(\Rightarrow D=\left(-\infty;-9\right)\cup\left(3;+\infty\right)\)
12 tháng 1
a: ĐKXĐ: 2x-4>0
=>2x>4
=>x>2
b: ĐKXĐ: 2x+8>0
=>2x>-8
=>x>-4
c: ĐKXĐ: 4-x>0
=>-x>-4
=>x<4
d: ĐKXĐ: \(\dfrac{1}{x+4}>0\)
=>x+4>0
=>x>-4
e: ĐKXĐ: \(\left(x-3\right)\left(x+9\right)>0\)
=>\(\left[{}\begin{matrix}x-3>0\\x+9< 0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x>3\\x< -9\end{matrix}\right.\)
2 tháng 2
bài 3:
\(A=\dfrac{9}{1\cdot2}+\dfrac{9}{2\cdot3}+\dfrac{9}{3\cdot4}+...+\dfrac{9}{2021\cdot2022}\)
\(=9\left(\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+...+\dfrac{1}{2021\cdot2022}\right)\)
\(=9\left(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{2021}-\dfrac{1}{2022}\right)\)
\(=9\cdot\dfrac{2021}{2022}=\dfrac{6063}{674}\)
Bài 1:
a: \(\left(\dfrac{1}{2}+\dfrac{16}{30}\right)-\left(1+\dfrac{1}{30}\right)\)
\(=\dfrac{15+16}{30}-1-\dfrac{1}{30}\)
\(=\dfrac{30}{30}-1\)
=1-1
=0
b: \(\dfrac{-5}{11}\cdot\dfrac{4}{13}+\dfrac{-5}{11}\cdot\dfrac{9}{13}+3\dfrac{5}{11}\)
\(=-\dfrac{5}{11}\left(\dfrac{4}{13}+\dfrac{9}{13}\right)+3+\dfrac{5}{11}\)
\(=-\dfrac{5}{11}+3+\dfrac{5}{11}\)
=3
c: \(3^2-12\left(\dfrac{3}{4}-\dfrac{2}{3}\right)\)
\(=9-12\cdot\dfrac{9-8}{12}\)
=9-1
=8
26 tháng 9 2021
a: \(\dfrac{-4}{3}\cdot\sqrt{\left(-0.4\right)^2}=\dfrac{-4}{3}\cdot\dfrac{2}{5}=\dfrac{-8}{15}\)
b: \(\sqrt[3]{\dfrac{3}{4}}\cdot\sqrt[3]{\dfrac{9}{16}}=\dfrac{3}{4}\)
a: \(log_2\dfrac{1}{16}=log_22^{-4}=-4\)
b: \(log_3243=log_33^5=5\)
c: \(9^{log_37}=7^{log_39}=7^2=49\)
c: \(\left(\dfrac{1}{81}\right)^{log_32}=\left(3^{-4}\right)^{log_32}=2^{log_33^{-4}}=2^{-4}=\dfrac{1}{16}\)
\(log_2\dfrac{1}{16}=-log_22^4=-4\)
\(log_3243=log_33^5=5\)
\(9^{log_37}=3^{2log_37}=3^{log_349}=49\)
\(\left(\dfrac{1}{81}\right)^{log_32}=3^{-4.log_32}=3^{log_32^{-4}}=2^{-4}=\dfrac{1}{16}\)