\(5^{x+3}-4.5^{x+1}=21.5\)
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a/|x|-2,5=27,5
=>|x|=27,5+2,5=30
=>x=30 hoặc x=-30
b/\(\dfrac{3}{4}+\dfrac{2}{5}.x=\dfrac{29}{60}\)
=>\(\dfrac{2}{5}.x\)=\(\dfrac{29}{60}-\dfrac{3}{4}\)=\(\dfrac{-4}{15}\)
=>x=\(\dfrac{-4}{15}:\dfrac{2}{5}\)=\(\dfrac{-2}{3}\)
c/(x-1)\(^5\)=-32
=>x-1=-2 vì (-2)\(^5\)=-32
=>x=-2+1=-1
d/\(\dfrac{4}{5}.x+0,5=4.5\)
=>\(\dfrac{4}{5}.x+0,5=20\)
=>\(\dfrac{4}{5}.x=20-0,5=19,5\)
=>\(x=19,5:\dfrac{4}{5}\)=\(\dfrac{195}{8}\)
c) {[(20 - 2.3).5] - 2.5} : 2 + (4.5)²
= {(20 - 6).5] - 10} : 2 + 20²
= (14.5 - 10) : 2 + 400
= (70 - 10) : 2 + 400
= 60 : 2 + 400
= 30 + 400
= 430
d) (1² + 2² + 3² + ... + 100²) . (2⁴ - 4²)
= (1² + 2² + 3² + ... + 100²) . (16 - 16)
= (1² + 2² + 3² + ... + 100²) . 0
= 0
Bài 2
a) -2x < 5
2x > 5
x > 5/2
b) [31 - (x + 5)].11 = 121
31 - (x + 5) = 121 : 11
31 - (x + 5) = 11
x + 5 = 31 - 11
x + 5 = 20
x = 20 - 5
x = 15
c) (x + 1)³ = 27
(x + 1)³ = 3³
x + 1 = 3
x = 3 - 1
x = 2
Tìm x
a) x - 1,27 = 13,5 : 4,5
x - 1,27 = 3
x = 1,27 + 3
x = 4,27
b) 8/3 - x = 2/5
x = 8/3 - 2/5
x = 34/15
Ta có: \(3\cdot5^{x+2}+4\cdot5^{x-3}=19\cdot5^{10}\)
\(\Leftrightarrow5^{x-3}\cdot\left(3\cdot5+4\right)=19\cdot5^{10}\)
\(\Leftrightarrow5^{x-3}\cdot19=19\cdot5^{10}\)
\(\Leftrightarrow5^{x-3}=5^{10}\)
\(\Rightarrow x-3=10\)
\(\Rightarrow x=13\)
\(5^{x+3}-4\cdot5^{x+1}=21\cdot5\)
\(\Rightarrow5^{x+1}\cdot5^2-4\cdot5^{x+1}=105\)\(\Rightarrow5^{x+1}\cdot\left(25-4\right)=105\)
\(\Rightarrow5^{x+1}\cdot21=105\) \(\Rightarrow5^{x+1}=5\) \(\Rightarrow x+1=1\) \(\Rightarrow x=0\)
5x+3 - 4 . 5x+1 = 21 . 5
=> 5x+1 . ( 52 - 4 ) = 21 . 5
=> 5x+1 . ( 25 - 4 ) = 21 . 51
=> 5x+1 . 21 = 21 . 51
=> 5x+1 = 51
=> x + 1 = 1
=> x = 0