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a) \(5^{x+3}+5^{x+1}-5^x=645\)
\(\Rightarrow5^x.5^3+5^x.5-5^x=645\)
\(\Rightarrow5^x.\left(5^3+5-1\right)=645\)
\(\Rightarrow5^x.129=645\)
\(\Rightarrow5^x=5\)
\(\Rightarrow x=1\)
Vậy \(x=1\)
b) \(9.27\ge3^x\ge243\)
\(\Rightarrow3^2.3^3\ge3^x\ge3^5\)
\(\Rightarrow3^5\ge3^x\ge3^5\)
\(\Rightarrow5\ge x\ge5\)
\(\Rightarrow x=5\)
Vậy \(x=5\)
a)(1/3)4-x=(1/4)3
1/81 -x =1/64
x= 1/81-1/64
x=-17/5184
b)(1/5) . x =(1/5)8 : (1/5)3
(1/5) . x =(1/5)5
x=(1/5)5 : (1/5)
x=(1/5)4
x=1/625
c)(2.x -3 )2=25
=> 2.x-3=5 hoặc =-5
nếu 2.x-3=5 nếu 2.x-3=-5
2.x=5+3 2.x=-5+3
2.x=8 2.x=-2
x=8/2=4 x=-2/2=-1
d)(3x+2)5=-243
(3x+2)5 =(-3)5
=>3x+2=-3
3x=-3+2
3x=-1
x=-1/3
c)(2x-3)\(^2\)=\(5^2\) hoặc(2x-3)\(^2\)=(-5)\(^2\) (2x-3)\(=5\) hoặc (2x-3)=(-5) 2x=8 hoặc 2x=-2 x=4 hoặc x=-1
a) \(\left(3x-2\right)^5=-243\)
\(\left(3x-2\right)^5=\left(-3\right)^5\)
\(3x-2=-3\)
\(3x=-3+2\)
\(3x=-1\)
\(x=-1:3\)
\(x=\dfrac{-1}{3}\)
b) \(3^{x+1}=9^x\)
\(3^{x+1}=\left(3^2\right)^x\) c)
\(3^{x+1}=3^{2x}\)
\(\Rightarrow x+1=2x\)
\(1=2x-x\)
\(1=x\)
Vậy x=1
b) \(3^{x+1}=9^x=3^{2x}\)
\(\Rightarrow x+1=2x\Leftrightarrow x=1\)
c) \(2^{3x+2}=4^x+5\Leftrightarrow4^{2x+1}=4^{x+5}\)
\(\Rightarrow2x+1=x+5\)\(\Rightarrow x=4\)
d) \(3^{2x-1}=243=3^5\)
\(\Rightarrow2x-1=5\Rightarrow x=3\)
( x - 1 )\(^5\) = -243
\(\Rightarrow\) ( x - 1 )\(^5\) = (- 3 )\(^5\)
\(\Rightarrow\) x - 1 = - 3
\(\Rightarrow\) x = -3 + 1
x = -2
Vậy x = -2
=> (x - 1)5 = (-3)5
=> x - 1 = -3
=> x = -2