\(5^x+5^{x+1}+5^{x-2}=151\)

\(5^{x-1}+5^{x-2}+5^{x-3}=155\)<...">

K
Khách

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7 tháng 7 2017

a, \(5^x+5^{x+1}+5^{x-2}=151\)

\(\Rightarrow5^x.\left(1+5+5^{-2}\right)=151\)

\(\Rightarrow5^x.6,04=151\Rightarrow5^x=25=5^2\)

\(5\ne-1;5\ne0;5\ne1\) nên \(x=2\)

b, \(5^{x-1}+5^{x-2}+5^{x-3}=155\)

\(\Rightarrow5^x.\left(5^{-1}+5^{-2}+5^{-3}\right)=155\)

\(\Rightarrow5^x.0,248=155\Rightarrow5^x=625=5^4\)

\(5\ne-1;5\ne0;5\ne1\) nên \(x=4\)

c, \(5^{2+x}+5^{3+x}=750\) \(\Rightarrow5^x.\left(5^2+5^3\right)=750\) \(\Rightarrow5^x.150=750\Rightarrow5^x=5=5^1\)\(5\ne-1;5\ne0;5\ne1\) nên \(x=1\) Chúc bạn học tốt!!!

\(•5^x+5^{x+1}+5^{x-2}=151\\ 5^x\left(1+5+\dfrac{1}{25}\right)=151\\ 5^x=25\\ \Rightarrow x=2\)

\(•5^{x-1}+5^{x-2}+5^{x-3}=155\\ 5^x.\left(\dfrac{1}{5}+\dfrac{1}{25}+\dfrac{1}{125}\right)=155\\ 5^x=625\\ \Rightarrow x=4\)

\(•5^{2+x}+5^{3+x}=750\\ 5^x\left(25+125\right)=750\\ 5^x=5\\ \Rightarrow x=1\)

12 tháng 1 2018

2, \(\Rightarrow\left\{{}\begin{matrix}\\\dfrac{5}{4}x-\dfrac{7}{2}=0\\\dfrac{5}{8}x+\dfrac{3}{5}=0\\\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{14}{5}\\\\x=\dfrac{-24}{25}\\\end{matrix}\right.\)

20 tháng 9 2016

thích làm mỗi câu d) mấy câu kia nhìn đã ớn rùi mà k thể hiện tư duy

d) = 2x + 2x.2 + 2x.22 + 2x.23 =120

       2x( 1+2+4+8) =120

2x = 120/15 =8 =23 

x =3

20 tháng 9 2016

a);b) dài lắm ,mk làm c) giúp bn thui, mk còn phải học bài

c) = (1/2)x + (1/2)x. (1/2)4 = 17

        (1/2)x(1 + 1/16) =17

(1/2)x = 1/16 = (1/2)4

x  = 4

14 tháng 2 2018

a) \(2\left(4x-30\right)-3\left(x+5\right)+4\left(x-10\right)=5\left(x+2\right)\)

\(\Leftrightarrow8x-60-3x+15+4x-40=5x+10\)

\(\Leftrightarrow9x-35=5x+10\)

\(\Leftrightarrow9x-5x=10+35\)

\(\Leftrightarrow4x=45\)

\(\Leftrightarrow x=\dfrac{45}{4}=11,25\)

b) \(\dfrac{11}{12}-\left(\dfrac{2}{5}+x\right)=\dfrac{2}{3}\left(6x+1\right)\)

\(\Leftrightarrow\dfrac{11}{12}-\left(\dfrac{2}{5}+x\right)=4x+\dfrac{2}{3}\)

\(\Leftrightarrow\dfrac{31}{60}+x=4x+\dfrac{2}{3}\)

\(\Leftrightarrow\dfrac{31}{60}-\dfrac{2}{3}=4x-x\)

\(\Leftrightarrow3x=\dfrac{1}{60}\)

\(\Leftrightarrow x=\dfrac{1}{180}\)

c) \(\dfrac{7}{3}-\left(2x-\dfrac{1}{3}\right)=\left(-2\dfrac{1}{6}+1\dfrac{1}{2}\right):0,25\)

\(\Leftrightarrow\dfrac{7}{3}-2x+\dfrac{1}{3}=-1\dfrac{2}{3}:\dfrac{1}{4}\)

\(\Leftrightarrow\dfrac{8}{3}-2x=\dfrac{-5}{3}.4\)

\(\Leftrightarrow\dfrac{8}{3}-2x=\dfrac{-20}{3}\)

\(\Leftrightarrow2x=\dfrac{8}{3}+\dfrac{20}{3}\)

\(\Leftrightarrow2x=\dfrac{28}{3}\)

\(\Leftrightarrow x=4\dfrac{2}{3}\)

d) \(0,75+\dfrac{5}{9}:x=5\dfrac{1}{2}\)

\(\Leftrightarrow\dfrac{3}{4}+\dfrac{5}{9}:x=\dfrac{11}{2}\)

\(\Leftrightarrow\dfrac{5}{9}:x=\dfrac{11}{2}-\dfrac{3}{4}\)

\(\Leftrightarrow\dfrac{5}{9}:x=\dfrac{19}{4}\)

\(\Leftrightarrow x=\dfrac{5}{9}:\dfrac{19}{4}\)

\(\Leftrightarrow x=\dfrac{20}{171}\)

29 tháng 8 2017

a) ta có : \(5^5-5^4+5^3=5^3.\left(5^2-5+1\right)=5^3.\left(25-5+1\right)\)

\(5^3.21=5^3.3.7⋮7\) (đpcm)

b) ta có : \(7^6+7^5-7^4=7^4.\left(7^2+7-1\right)=7^4.\left(49+7-1\right)\)

\(=7^4.55=7^4.5.11⋮11\) (đpcm)

c) ta có : \(3^{x+2}-2^{x+3}+3^x-2^{x+1}=3^{x+2}+3^x-2^{x+3}-2^{x+1}\)

\(=3^x\left(3^2+1\right)-2^x\left(2^3+2\right)=3^x.\left(9+1\right)-2^x.\left(8+2\right)\)

\(=3^x.10-2^x.10=10\left(3^x-2^x\right)⋮10\) (đpcm)

d) \(3^{x+3}+3^{x+1}+2^{x+3}+2^{x+2}=3^x.\left(3^3+3\right)+2^x.\left(2^3+2^2\right)\)

\(=3^x.\left(27+3\right)+2^x\left(8+4\right)=3^x.30+2^x.12=6.\left(3^x.5+2^x.2\right)⋮6\) (đpcm)

29 tháng 8 2017

a)Ta có:\(5^5-5^4+5^3=5^3\left(5^2-5+1\right)=5^3.21\)(vì 21 chia hết cho 7)

\(\)\(\RightarrowĐPCM\)

b)Ta có: \(7^6+7^5-7^4⋮11=7^4\left(7^2+7-1\right)=7^4.55⋮11\)

\(\Rightarrowđpcm\)