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a: 18:(x-3)=6
=>x-3=18:6=3
=>x=3+3=6
b: \(3^{x-1}+4=85\)
=>\(3^{x-1}=81\)
=>\(3^{x-1}=3^4\)
=>x-1=4
=>x=5
c: 2x+3x=55
=>5x=55
=>x=55/5=11
d: \(\left(x-3\right)^3+11=53\)
=>\(\left(x-3\right)^3=53-11=42\)
=>\(x-3=\sqrt[3]{42}\)
=>\(x=\sqrt[3]{42}+3\)
a) 18 : (x - 3) = 6
x - 3 = 18 : 6
x - 3 = 3
x = 3 + 3
x = 6
b) 3ˣ⁻¹ + 4 = 85
3ˣ⁻¹ = 85 - 4
3ˣ⁻¹ = 81
3ˣ⁻¹ = 3⁴
x - 1 = 4
x = 4 + 1
x = 5
c) 2x + 3x = 55
5x = 55
x = 55 : 5
x = 11
d) Sửa đề:
(x - 3)³ - 11 = 53
(x - 3)³ = 53 + 11
(x - 3)³ = 64
(x - 3)³ = 4³
x - 3 = 4
x = 4 + 3
x = 7
2:
=>27:3^x=2*25-16-31=50-47=3
=>3^x=27/3=9
=>3^x=3^2
=>x=2
1:
b: \(=16\cdot55+16\cdot45-1\)
=16(55+45)-1
=1600-1
=1599
c: \(=\dfrac{1800}{49-\left[2\cdot\left(36-34\right)^3-5\right]}\)
\(=\dfrac{1800}{49-2\cdot2^3+5}=\dfrac{1800}{49-16+5}=\dfrac{1800}{38}\)=900/19
d: \(=\dfrac{5\cdot3^{11}\cdot2^{11}-3^{11}\cdot2^{11}}{2^{10}\cdot3^{10}\cdot2^2\cdot3+7\cdot2^{12}\cdot3^{12}}\)
\(=\dfrac{3^{11}\cdot2^{11}\left(5-1\right)}{2^{12}\cdot3^{11}\left(1+7\cdot3\right)}=\dfrac{1}{2}\cdot\dfrac{4}{1+21}=\dfrac{4}{22\cdot2}=\dfrac{1}{11}\)
\(\Rightarrow\dfrac{2x}{6}=\dfrac{3y}{6}=\dfrac{z}{6}\Rightarrow\dfrac{x}{3}=\dfrac{y}{2}=\dfrac{z}{6}=\dfrac{x+y+z}{3+2+6}=\dfrac{11}{11}=1\\ \Rightarrow\left\{{}\begin{matrix}x=3\\y=2\\z=6\end{matrix}\right.\Rightarrow z-x=6-3=3\left(A\right)\)