\(5^{2.x-3}-2.5^2=5^2.3\)
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1) \(7.4^x=7.4^3\Leftrightarrow4^x=4^3;x=3\)
2) \(\frac{3}{2.5^x}=\frac{3}{2.5^{12}}\Leftrightarrow5^x=5^{12};x=12\)
\(2^x=2.2^8=2^9;x=9\)
4) \(5.3^x=7.3^5-2.3^5\Leftrightarrow5.3^x=3^5.\left(7-2\right)\)
\(\Leftrightarrow3^5.x=3^5.5;x=5\)
5^(2x-3) = 5^2.3 + 2.5^2
5^(2x-3) = 5^2( 3 + 2)
5^(2x-3) = 5^2.5
5^(2x-3) = 5^3
2x - 3 =3
2x = 6
x = 3
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
\(5^{2x-3}-2\cdot5^2=5^2\cdot3\)
\(\Rightarrow5^{2x-3}-50=75\)
\(\Rightarrow5^{2x-3}=75+50\)
\(\Rightarrow5^{2x-3}=125\)
\(\Rightarrow5^{2x-3}=5^3\)
\(\Rightarrow2x-3=3\)
\(\Rightarrow2x=6\)
\(\Rightarrow x=\dfrac{6}{2}=3\)
25x-3-2.25=25.3
25x-3-50=75
25x-53=75
25x=75+53
25x=128
x=128
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25
25x-3-2.25=25.3
25x-3-50=75
25x-53=75
25x=75+53
25x=128
x=128
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25
\(5^{2x-3}-2\times5^2=5^2\times3\)
\(5^{2x-3}=5^2\times3+2\times5^2\)
\(5^{2x}:5^3=5^2\left(3+2\right)\)
\(5^{2x}=5^6\)
\(\Rightarrow2x=6\)
x= 3