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\(3^{x+2}-3^x=72\)
\(\Rightarrow3^x\cdot\left(3^2-1\right)=72\)
\(\Rightarrow3^x\cdot\left(9-1\right)=72\)
\(\Rightarrow3^x\cdot8=72\)
\(\Rightarrow3^x=\dfrac{72}{8}\)
\(\Rightarrow3^x=9\)
\(\Rightarrow3^x=3^2\)
\(\Rightarrow x=2\)
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Xem lại đề
![](https://rs.olm.vn/images/avt/0.png?1311)
\(72^{45}-72^{44}=72^{44}.\left(72-1\right)=72^{44}.71\)
\(72^{44}-72^{43}=72^{43}.\left(72-1\right)=72^{43}.71\)
Vì \(72^{44}>72^{43}\Rightarrow72^{45}-72^{44}>72^{44}-72^{43}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a) \(\frac{5}{12}=\frac{x}{72}\Rightarrow x=\frac{5.72}{12}=30\)
b)\(\frac{x+3}{15}=\frac{1}{3}\)
\(\Rightarrow x+3=\frac{15.1}{3}=5\)
\(\Rightarrow x=5-3=2\)
c)\(\frac{-2}{9}=\frac{x}{72}\Rightarrow x=\frac{-2.72}{9}=-16\)
![](https://rs.olm.vn/images/avt/0.png?1311)
x-2/12 + x-2/20+....+x-2/72
=x-2/3.4+ x-2/ 4.5+...+x-2/8.9
=(x-2).1/3.4.1+(x-2).1/4.5.1+......+(x-2).1/8.9.1
=x-2/1(1/3.4+1/4.5+....+1/8.9)
=x-2(1/3 -1/4 +1/4 -1/5+...+1/8-1/9)
=x-2(1/3-1/9)
=(x-2).2/9
=2x-4/9
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Câu 3:
\(2S=2+2^2+2^3+...+2^{10}\)
nên \(S=2^{10}-1\)
\(5\cdot2^8=256\cdot5=1280>1023=2^{10}-1\)
Do đó: \(S< 5\cdot2^8\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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2.
a, x-13=-46
=>x=(-46)+13
=>x=33
b, 4x-6=22
=>4x=22+6
=>4x=28
=>x=28:4
=>x=7
3.
a, 32=25
48=24.3
=>ƯCLN(32,48)=24=16
16=24
72=23.32
=>ƯCLN(16,72)=23=8
b,
24=23.3
60=22.3.5
=>BCNN(24,60)=23.3.5=120
72=23.32
180=22.32.5
=>BCNN(72,180)=23.32.5=360
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