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e) \(\left(2x-15\right)^5=\left(2x-15\right)^3\)
\(\Rightarrow\left(2x-15\right)^5-\left(2x-15\right)^3=0\)
\(\Rightarrow\left(2x-15\right)^3\cdot\left(2x-15\right)^2-\left(2x-15\right)^3=0\)
\(\Rightarrow\left(2x-15\right)^3\cdot\left[\left(2x-15\right)^2-1\right]=0\)
\(\Rightarrow\left(2x-15\right)^3=0\) hoặc \(\left(2x-15\right)^2-1=0\)
+)TH1: \(\left(2x-15\right)^3=0\)
\(\Rightarrow2x-15=0\)
\(\Rightarrow2x=15\)
\(\Rightarrow x=\frac{15}{2}\)
+)TH2: \(\left(2x-15\right)^2-1=0\)
\(\Rightarrow\left(2x-15\right)^2=1\)
\(\Rightarrow\left[{}\begin{matrix}2x-15=1\\2x-15=-1\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}2x=16\\2x=14\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=8\\x=7\end{matrix}\right.\)
Vậy \(x=\frac{15}{2}\) hoặc \(x=8\) hoặc \(x=7\)
a) \(2^x-17=15\Rightarrow2^x=32\)
Mà \(2^5=32\Rightarrow x=5\)
Vậy x = 5
b)\(\left(7x-11\right)^3=2^5\cdot5^2+200\)
\(\Rightarrow\left(7x-11\right)^3=1000\)
\(\Rightarrow\left(7x-11\right)^3=10^3\)
\(\Rightarrow7x-11=10\)
\(\Rightarrow7x=21\)
\(\Rightarrow x=3\)
Vậy x = 3
c)\(x^{10}=1^x\Rightarrow x^{10}=1\)(số 1 có luỹ thừa là bao nhiêu thì vẫn là 1 thui)\(\Rightarrow x=1\)
Vậy x = 1
d) \(x^{10}=x\Rightarrow x^{10}-x=0\)
\(\Rightarrow x\left(x^9-1\right)=0\)
\(\Rightarrow x=0\) hoặc \(x^9-1=0\)
+)TH1: \(x=0\)
+)TH2: \(x^9-1=0\Rightarrow x^9=1\Rightarrow x=1\)
Vậy x = 0 hoặc x = 1
a) 2x - 15 = 17
2x = 25
b) ( 7x - 11 )3 = 25. 52 + 200
(7x - 11)3 = 32 . 25 + 200
(7x -11)3 = 1000
(7x-11)3 = 103
7x - 11 = 10
7x = 10+11
7x = 21
x = 21 : 7
x = 3
like nha
\(\left(3x-1\right)^3=25\left(3x-1\right)\\ \Leftrightarrow\left(3x-1\right)^2=25\\ \Leftrightarrow\left[{}\begin{matrix}3x-1=5\\3x-1=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-\dfrac{4}{3}\end{matrix}\right.\\ \left(3x-14\right)^3=2^5\cdot5^2+200\\ \Leftrightarrow\left(3x-14\right)^3=1000=10^3\\ \Leftrightarrow3x-14=10\Leftrightarrow x=8\)
\(\left(3x-1\right)^3=25\left(3x-1\right)\)
\(\Rightarrow\left(3x-1\right)\left(9x^2-6x+1-25\right)=0\)
\(\Rightarrow\left(3x-1\right)\left(9x^2-6x-24\right)=0\)
\(\Rightarrow3\left(3x-1\right)\left(x-2\right)\left(3x+4\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{3}\\x=2\\x=-\dfrac{4}{3}\end{matrix}\right.\)
\(\left(3x-14\right)^3=2^5.5^2+200\)
\(\Rightarrow\left(3x-14\right)^3=1000\)
\(\Rightarrow3x-14=10\Rightarrow3x=24\Rightarrow x=8\)
= \(\frac{3^2.5^4.7^9}{3^3.5^2.7^5.3^3.5^2.7^5}\)
=\(\frac{3^2.5^4.7^9}{3^6.5^4.7^{10}}\)
= \(\frac{1.1.1}{3^4.1.7}\)
= \(\frac{1}{567}\)
\(\frac{\left(3^2.5.7^9\right).\left(3^5.5^3\right)}{\left(3^3.5^2.7^5\right)^2}=\frac{\left(3^2.3^5\right).\left(5.5^3\right).7^9}{3^6.5^4.7^{10}}=\frac{3^7.5^4.7^9}{3^6.5^4.7^{10}}=\frac{3}{7}\)
a.=\(\dfrac{4^3.9^3.5^44^4.18^2}{4^5.9^5.5^5}\)=\(\dfrac{4^4.9^2.2^2}{4^2.9^2.5}\)=\(\dfrac{4^2.2^2}{5}\)=\(\dfrac{64}{5}\)
Bài 2:
a) (2x+1)3 = 27
(2x+1)3 = 33
=> 2x+1 = 3
=> 2x = 2
=> x = 1
a, \(\left(x-1\right)^3=125\)
\(\Rightarrow x-1=5\Rightarrow x=6\)
b, \(\left(2x+1\right)^3=343\)
\(\Rightarrow2x+1=7\Rightarrow x=3\)
c, \(\left(7x-11\right)^3=2^5.5^2+200\)
\(\Rightarrow\left(7x-11\right)^3=32.25+200\)
\(\Rightarrow\left(7x-11\right)^3=1000\)
\(\Rightarrow7x-11=10\Rightarrow x=3\)
Chúc bạn học tốt!!!
a) \(\left(x-1\right)^3=125\Leftrightarrow\left(x-1\right)^3=5^3\Rightarrow x-1=5\)
\(\Leftrightarrow x=6\) vậy \(x=6\)
b) \(\left(2x+1\right)^3=343\Leftrightarrow\left(2x+1\right)^3=7^3\Rightarrow2x+1=7\)
\(\Leftrightarrow2x=6\Leftrightarrow x=\dfrac{6}{2}=3\) vậy \(x=3\)
c) \(\left(7x-11\right)^3=2^5.5^2+200\Leftrightarrow\left(7x-11\right)^3=32.25+200\)
\(\Leftrightarrow\left(7x-11\right)^3=800+200=1000=10^3\Rightarrow7x-11=10\)
\(\Leftrightarrow7x=21\Leftrightarrow x=\dfrac{21}{7}=3\) vậy \(x=3\)
\(5.5^{2x+1}=\left(5^2\right)^2\)
\(5.5^{2x}.5=5^4\)
\(5^2.5^{2x}=5^4\)
\(5^{2x}=5^4:5^2\)
\(5^{2x}=5^2\)
\(\Rightarrow x=1\)
#Hoc tot!!!
~NTTH~
\(5.5^{2x+1}=\left(5^2\right)^2\)
=> \(5^{2x+2}=\left(5^2\right)^2\)
=> \(5^{x+1}.5^2=5^2.5^2\)
=> \(5^{x+1}=5^2\)
=> \(x+1=2\)
=> \(x=1\)