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22 tháng 10 2019
1. \(6x^3-8=40\\ 6x^3=48\\ x^3=8\\ \Rightarrow x=2\)Vậy x = 2
2. \(4x^5+15=47\\ 4x^5=32\\ x^5=8\\ \Rightarrow x\in\varnothing\left(\text{vì }x\in N\right)\)Vậy x ∈ ∅
3. \(2x^3-4=12\\ 2x^3=16\\ x^3=8\\ \Rightarrow x=2\)Vậy x = 2
4. \(5x^3-5=0\\ 5x^3=5\\ x^3=1\\ \Rightarrow x=1\)Vậy x = 1
5. \(\left(x-5\right)^{2016}=\left(x-5\right)^{2018}\\ \Rightarrow\left[{}\begin{matrix}x-5=0\\x-5=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=5\\x=6\end{matrix}\right.\)Vậy \(x\in\left\{5;6\right\}\)
6. \(\left(3x-2\right)^{20}=\left(3x-1\right)^{20}\\ \Rightarrow3x-2=3x-1\\ 3x-3x=2-1\\ 0=1\left(\text{vô lí}\right)\)Vậy x ∈ ∅
7. \(\left(3x-1\right)^{10}=\left(3x-1\right)^{20}\\ \left(3x-1\right)^{10}=\left[\left(3x-1\right)^2\right]^{10}\\ \Rightarrow\left(3x-1\right)^2=3x-1\\ \left(3x-1\right)^2-\left(3x-1\right)=0\\ \left(3x-1\right)\left[\left(3x-1\right)-1\right]=0\\ \left(3x-1\right)\left(3x-2\right)=0\\ \Rightarrow\left[{}\begin{matrix}3x-1=0\\3x-2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}3x=1\\3x=2\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\frac{1}{3}\left(\text{loại vì }x\in N\right)\\x=\frac{2}{3}\left(\text{loại vì }x\in N\right)\end{matrix}\right.\)Vậy x ∈ ∅
8. \(\left(2x-1\right)^{50}=2x-1\\ \left(2x-1\right)^{50}-\left(2x-1\right)=0\\ \left(2x-1\right)\left[\left(2x-1\right)^{49}-1\right]=0\\ \Rightarrow\left[{}\begin{matrix}2x-1=0\\\left(2x-1\right)^{49}=1\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}2x=1\\2x-1=1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\frac{1}{2}\left(\text{loại vì }x\in N\right)\\x=1\left(t/m\right)\end{matrix}\right.\)Vậy x = 1
9. \(\left(\frac{x}{3}-5\right)^{2000}=\left(\frac{x}{3}-5\right)^{2008}\\ \left(\frac{x}{3}-5\right)^{2008}-\left(\frac{x}{3}-5\right)^{2000}=0\\ \left(\frac{x}{3}-5\right)^{2000}\left[\left(\frac{x}{3}-5\right)^8-1\right]=0\\ \Rightarrow\left[{}\begin{matrix}\left(\frac{x}{3}-5\right)^{2000}=0\\\left(\frac{x}{3}-5\right)^8=1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}\frac{x}{3}-5=0\\\frac{x}{3}-5=1\\\frac{x}{3}-5=-1\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}\frac{x}{3}=5\\\frac{x}{3}=6\\\frac{x}{3}=4\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=5\cdot3=15\\x=6\cdot3=18\\x=4\cdot3=12\end{matrix}\right.\)Vậy \(x\in\left\{15;18;12\right\}\)
22 tháng 10 2019
\(1.6x^3-8=40\\ \Leftrightarrow6x^3=48\\ \Leftrightarrow x^3=8\Leftrightarrow x^3=2^3=\left(-2\right)^3\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\)
Vậy \(x\in\left\{2;-2\right\}\)
\(2.4x^3+15=47\) (T nghĩ đề là mũ 3)
\(\Leftrightarrow4x^3=32\Leftrightarrow x^3=8=2^3=\left(-2\right)^3\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\)
Vậy \(x\in\left\{2;-2\right\}\)
Câu 3, 4 tương tự nhé.
22 tháng 12 2017
a,\(5^3.2-100:4+2^3.5\)
= 125 . 2 - 25 + 8 . 5
= 250 - 25 + 40
= 265
b, \(6^2:9+50.2-3^3.3\)
= 36 : 9 + 100 - 27 . 3
= 4 + 100 - 81
= 23
KT
24 tháng 8 2018
\(4^8.2^{20}=2^{16}.2^{20}=2^{36}\)
\(9^{12}.27^5.81^4=3^{24}.3^{15}.3^{16}=3^{55}\)
mk chỉnh đề
\(64^3.4^5.16^2=4^9.4^5.4^4=4^{18}\)
\(25^{20}.125^4=5^{40}.5^{12}=5^{52}\)
\(x^7.x^4.x^3=x^{14}\)
6 tháng 3 2020
a)\(\frac{3^{10}.\left(-5\right)^{21}}{\left(-5\right)^{20}.3^{12}}=\frac{-5}{9}\)
b)\(\frac{\left(-11\right)^5.13^7}{11^5.13^8}=-\frac{1}{13}\)
c)\(\frac{2^{10}.3^{10}-2^{10}.3^9}{2^9.3^{10}}=\frac{2^{10}.3^9\left(3-1\right)}{2^9.3^{10}}=2\)
d(\(\frac{5^{11}.7^{12}+5^{11}.7^{11}}{5^{12}.7^{12}+9.5^{11}.7^{11}}=\frac{5^{11}.7^{11}\left(7+1\right)}{5^{11}.7^{11}\left(35+9\right)}=\frac{1}{6}\)
SN
12 tháng 10 2018
a,
15^12=(3*5)^12=3^12*5^12
81^3*125^5=(3^4)^3*(5^3)^5=3^12*5^15
Vì 12<15 suy ra 5^12<5^15
Suy ra 3^12*5^12<3^12*5^15
T
12 tháng 10 2018
\(a.81^3.125^5=\left(3^4\right)^3.\left(5^3\right)^5=3^{12}.5^{15}=3^{12}.5^{12}.5^3=\left(3.5\right)^{12}.5^3=15^{12}.5^3>15^{12}\)
\(b.4^{20}.81^{12}=\left(2^2\right)^{20}.\left(9^2\right)^{12}=2^{40}.9^{24}=2^{20}.2^{20}.9^{20}.9^4=\left(2.9\right)^{20}.2^{20}.9^4=18^{20}.2^{20}.9^4>18^{20}\)
\(c.73^{75}=\left(73^3\right)^{25}=389017^{25}\)
\(107^{50}=107^{2.50}=\left(107^2\right)^{25}=11449^{25}\)
Vì \(389017^{25}>11449^{25}\Rightarrow73^{75}>107^{50}\)
9 tháng 4 2020
a, \(\frac{6^5\cdot27^2}{7^3\cdot9^5}=\frac{2^5\cdot3^5\cdot\left(3^3\right)^2}{7^3\cdot\left(3^2\right)^5}=\frac{2^5\cdot3^5\cdot3^6}{7^3\cdot3^{10}}=\frac{2^5\cdot3^{11}}{7^3\cdot3^{10}}=\frac{2^5\cdot3}{7^3}\)
b, \(\frac{12^7\cdot9^3}{8^5\cdot27^3}=\frac{3^7\cdot2^{12}\cdot3^6}{2^{15}\cdot3^9}=\frac{2^{12}\cdot3^{13}}{2^{15}\cdot3^9}=\frac{3^4}{2^3}\)
c, \(\frac{20^6\cdot8^2}{16^3\cdot25^3}=\frac{2^{12}\cdot5^6\cdot2^6}{2^{12}\cdot5^6}=2^6\)
16 tháng 12 2023
1: \(78+22+18\)
\(=\left(78+22\right)+18\)
=100+18
=118
2: \(94+563+\left(106-563\right)-\left(-70\right)\)
\(=94+563+106-563+70\)
\(=\left(94+106\right)-\left(563-563\right)+70\)
=100-0+70
=170
3: \(25\cdot154-25+47\cdot25\)
\(=25\left(154-1+47\right)\)
\(=25\cdot200=5000\)
4: \(\left[5^{29}+5^{30}\left(16-11\right)\right]:5^{29}\)
\(=\left(5^{29}+5^{30}\cdot5\right):5^{29}\)
\(=\dfrac{5^{29}\cdot1+5^{29}\cdot5^2}{5^{29}}\)
\(=1+5^2=26\)
8: \(25\cdot2^3-\left(9-14\right)+\left(29-34+20\right)\)
\(=25\cdot8-\left(-5\right)+\left(-5\right)+20\)
\(=200+5-5+20\)
=220
đề bài?
350 = 295245 570= 68359375 920= 6973568802 520= 19531250