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1/2.2x+4.2x=9.2x
2x.(1/2+4)=9.2x
2x.9/2=9.2x
2x:2x=9:9/2
x=2
vậy x=2
a)7.2x=56⇔2x=8⇔2x=23⇔x=3
b)(2x+1)3=9.81⇔(2x+1)3=93⇔2x+1=9⇔2x=8⇔x=4
c)x3=82⇔x3=26⇔x=22⇔x=4
d)4.2x-3=1⇔4.2x=4⇔2x=1⇔2x=20⇔x=0
e)2.3x=162⇔3x=81⇔3x=34⇔x=4
a) (x: 8 - l).2 = 1.14 nên x : 8 - 1 = 7. Do đó x = 64.
b) (2x + 3).30 = 25.6 nên 2x + 3 = 5. Do đó x = 1.
c) 6.(2x - 7) = 9.(x - 3) nên 12x - 42 = 9x - 27.
Do đó 3x = 15. Vậy x = 5.
d) -7.(x + 27) = 6.(x + l) nên -7x - 189 = 6x + 6.
Do đó 13x = -195. Vậy x = -15.
\(\Leftrightarrow3\left(2x-1\right)+5⋮2x-1\\ \Leftrightarrow2x-1\inƯ\left(5\right)=\left\{-5;-1;1;5\right\}\\ \Leftrightarrow x\in\left\{-2;0;1;3\right\}\)
\(6x+4x-2x=2010\)
\(10x-2x=2010\)
\(8x=2010\)
\(\Rightarrow x=\frac{1005}{4}=251,25\)
d) \(\left(7-2x\right)^2=49\)
\(\Rightarrow\left(7-2x\right)^2=\left(\pm7\right)^2\)
\(\Rightarrow\left[{}\begin{matrix}7-2x=7\\7-2x=-7\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x=7-7\\2x=7+7\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x=0\\2x=14\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=7\end{matrix}\right.\)
e) \(\left(9-x\right)^3=216\)
\(\Rightarrow\left(9-x\right)^3=6^3\)
\(\Rightarrow9-x=6\)
\(\Rightarrow x=9-6\)
\(\Rightarrow x=3\)
g) \(6^{x+2}+6^x=1332\)
\(\Rightarrow6^x\cdot\left(6^2+1\right)=1332\)
\(\Rightarrow6^x\cdot37=1332\)
\(\Rightarrow6^x=1332:37\)
\(\Rightarrow6^x=36\)
\(\Rightarrow6^x=6^2\)
\(\Rightarrow x=2\)
\(d,\left(7-2x\right)^2=49\)
\(\Leftrightarrow\left[{}\begin{matrix}7-2x=7\\7-2x=-7\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=0\\2x=14\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=7\end{matrix}\right.\)
\(e,\left(9-x\right)^3=216\)
\(\Leftrightarrow\left(9-x\right)^3=6^3\)
\(\Leftrightarrow9-x=6\)
\(\Leftrightarrow x=3\)
\(f,6^{x+2}+6^x=1332\)
\(\Leftrightarrow6^x\left(6^2+1\right)=1332\)
\(\Leftrightarrow6^x\cdot37=1332\)
\(\Leftrightarrow6^x=36\)
\(\Leftrightarrow6^x=6^2\)
\(\Leftrightarrow x=2\)
#Urushi
Ta có:
\(\left(6x+2\right)⋮\left(2x-1\right)\Leftrightarrow\left[3\left(2x-1\right)+5\right]⋮\left(2x-1\right)\)
\(\Leftrightarrow5⋮\left(2x-1\right)\Leftrightarrow2x-1\inƯ\left(5\right)=\left\{-5;-1;1;5\right\}\)
\(\Rightarrow x\in\left\{-2;0;1;3\right\}\)
6x + 6x+1 = 2x + 2 . 2x + 4 . 2x
=> 6x . ( 1 + 6 ) = 2x . ( 1 + 2 + 4 )
=> 6x . 7 = 2x . 7
=> 6x = 2x
Xét 2 trường hợp :
+) x = 0
=> 60 = 20
=> 1 = 1 ( thỏa mãn )
+) x ≥ 0
Ta có : \(\hept{\begin{cases}6^x⋮3∀x\ge1\\2^x⁒3∀x\ge1\end{cases}}\)=> x ∈ Ø