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Ta có : 3x + 1 - 3x = 54
\(\Rightarrow\)3x . 3 - 3x = 54
\(\Rightarrow\)3x.( 3 - 1 ) = 54
\(\Rightarrow\)3x . 2 = 54
\(\Rightarrow\)3x = 27 = 33
\(\Rightarrow\)x = 3
Vậy : x = 3
b; 2\(^x\) = 4.128
2\(^x\) = 512
2\(^x\) = 29
\(x\) = 9
Vậy \(x\) = 9
c; 2\(^x\).3\(^x\) = 4.9
6\(^x\) = 36
6\(^x\) = 62
\(x=2\)
Vậy \(x=2\)
a) 120 - 5 . ( x + 2 ) = 45
5 . (x + 2) = 120 - 45
5 . (x + 2) = 75
x + 2 = 75 : 5
x + 2 = 15
x = 17
b) ( 2.x - 3 )2 = 49
( 2.x - 3 )2 = 72
( 2.x - 3 ) = 7
2x = 10
x = 5
a) \(5^{x+1}=125=5^3\)
\(\Rightarrow x+1=3\Rightarrow x=2\)
b) \(\left(x-16\right)^2=9=3^2\)
\(\Rightarrow x-16=3\Rightarrow x=19\)
d) \(\left(x-1\right)^2=\left(x-1\right)^3\)
\(\Rightarrow\orbr{\begin{cases}x-1=0\\x-1=1\end{cases}\Rightarrow\orbr{\begin{cases}x=1\\x=2\end{cases}}}\)
Bài 1 :
a) 5x = 125
=> 5x = 53
=> x = 3
b) 34 . 3x = 37
=> 4 + x = 7
=> x = 7 - 4
=> x = 2
a) (x54)2=x
x108=x
x108: x=0
x108-1=0
x107=0
=>x=0
vậy x=0
b)2x+3+2x=144
2x.23+2x=144
2x.(23+1)=144
2x.(8+1)=144
2x.9=144
2x=144:9
2x=16
2x=24
=>x=4
vậy x=4
\(a.\)\(\left(x^{54}\right)^2=x\)
\(\Leftrightarrow x^{108}=x\)
\(\Leftrightarrow x^{108}-x=0\)
\(\Leftrightarrow x.\left(x^{107}-1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x^{107}-1=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x^{107}=1\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}\)
\(b.\)\(2^{x+3}+2^x=144\)
\(\Leftrightarrow2^x.2^3+2^x.1=144\)
\(\Leftrightarrow2^x.\left(2^3+1\right)=144\)
\(\Leftrightarrow2^x.9=144\)
\(\Leftrightarrow2^x=144:9\)
\(\Leftrightarrow2^x=16\)
\(\Leftrightarrow2^x=2^4\)
\(\Leftrightarrow x=4\)
\(3^x-3^{x-1}=54\)
=>\(3^x-\dfrac{1}{3}\cdot3^x=54\)
=>\(\dfrac{2}{3}\cdot3^x=54\)
=>\(3^x=54:\dfrac{2}{3}=81=3^4\)
=>x=4