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\(2^{x+2}\cdot3^{x+1}\cdot5x=10800\)
\(2^x\cdot2^2\cdot3^x\cdot2\cdot5^x=10800\)
\(\left(2\cdot3\cdot5\right)^x\cdot12=10800\)
\(30^x=10800\div12\)
\(30^x=900\)
\(\Leftrightarrow30^{x=}=30^2\Leftrightarrow x=2\)
<=> 2x.22.3x.31.5x=10800
<=> 30x = 900
<=> 30x = 302
=> x = 2
Bạn chỉ mình cách gõ số mũ rồi mình giải cho
Ta có : \(10800=2^4.3^3.5^2\)
\(\Rightarrow2^{x+2}.3^{x+1}.5^x=2^4.3^3.5^2\Rightarrow x=2.\)
2x+2.3x+1.5x=10800
2x.22.3x.2.5x=10800
(2.3.5)x.12=10800
30x=10800:12
30x=900
\(30^{^{ }m}\)\(30^2\Rightarrow x=2\)
a) x - 3/97 + x - 2/98 = x - 1/99 + x/100
<=> x + 1/99 + 1 + x + 2/98 + 1 + x + 3/97 + 1 + (x + 4/96 + 1 + x + 5/95 + 1 + x + 10/90 + 1) = 0
<=> x + 100/99 + x + 100/98 + x + 100/97 + (x + 100/96 + x + 100/95 + x + 100/90) = 0
<=> (x + 100)(1/99 + 1/98 + 1/97 + 1/96 + 1/95 + 1/90) = 0
Mà 1/99 + 1/98 + 1/97 + 1/96 + 1/95 + 1/90 khác 0
=> x + 100 = 0
=> x = -100
c) (1/1.2 + 1/2.3 + ... + 1/99.100) - 2x = 1/2
<=> (1 - 1/2 + 1/2 - 1/3 + ... + 1/99 - 1/100) - 2x = 1/2
<=> (1 - 1/100) - 2x = 1/2
<=> 99/100 - 2x = 1/2
<=> -2x = 1/2 - 99/100
<=> -2x = -49/100
<=> x = 49/200
=> x = 49/200
\(\frac{x+2}{327}+\frac{x+3}{326}+\frac{x+4}{325}+\frac{x+5}{324}+\frac{x+349}{5}=0\)
\(\Rightarrow\left(\frac{x+2}{327}+1\right)+\left(\frac{x+3}{326}+1\right)+\left(\frac{x+4}{325}+1\right)+\left(\frac{x+5}{324}+1\right)+\left(\frac{x+349}{5}-4\right)=0\)
\(\Rightarrow\frac{x+329}{327}+\frac{x+329}{326}+\frac{x+329}{325}+\frac{x+329}{324}+\frac{x+329}{5}=0\)
\(\Rightarrow\left(x+329\right)\left(\frac{1}{327}+\frac{1}{326}+\frac{1}{325}+\frac{1}{324}+\frac{1}{5}\right)=0\)
Dễ thấy \(\frac{1}{327}+\frac{1}{326}+\frac{1}{325}+\frac{1}{324}+\frac{1}{5}>0\Rightarrow x+329=0\)
\(\Rightarrow x=-329\)