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\(a,\left(7x-11\right)^3=2^5.5^2+200.\)
\(\left(7x+11\right)^3=32.25+200.\)
\(\left(7x+11\right)^3=800+200.\)
\(\left(7x-11\right)^3=1000.\)
\(\left(7x-11\right)^3=10^3.\)
\(\Rightarrow7x-11=10.\)
\(\Rightarrow x=\left(10+11\right):3=7\in Z.\)
Vậy.....
\(b,3^x+25=26.2^2+2.3^0.\)
\(3^x+25=26.4+2.\)
\(3^x+25=104+2.\)
\(3^x+25=106.\)
\(3^x=106-25.\)
\(3^x=81.\)
\(3^x=3^4\Rightarrow x=4\in Z.\)
Vậy.....
\(c,2^x+3.2=64.\)(có vấn đề).
\(d,5^{x+1}+5^x=750.\)
\(5^x.5^1+5^x+1=750.\)
\(5^x\left(5^1+1\right)=750.\)
\(5^x\left(5+1\right)=750.\)
\(5^x.6=750.\)
\(5^x=750:6.\)
\(5^x=125.\)
\(5^x=5^3\Rightarrow x=3\in Z.\)
Vậy.....
\(e,x^{15}=x.\)
\(\Rightarrow x\left(x^{14}-1\right)=0\Rightarrow\left\{{}\begin{matrix}x=0\\x=1\end{matrix}\right..\)
\(f,\left(x-5\right)^4=\left(x-5\right)^6.\)
\(\Leftrightarrow\left(x-5\right)^4-\left(x-5^6\right)=0.\)
\(\Leftrightarrow\left(x-5\right)^4\left[1-\left(x-5\right)^2\right]=0.\)
\(\Leftrightarrow\left(x-5\right)^4\left(1-x+5\right)\left(1+x-5\right)=0.\)
\(\Leftrightarrow\left(x-5\right)^4\left(6-x\right)\left(x-4\right)=0.\)
\(\Leftrightarrow\left(x-5\right)^4=0\Rightarrow x-5=0\Rightarrow x=5\in Z.\)
\(6-x=0\Rightarrow x=6\in Z.\)
\(x-4=0\Rightarrow x=4\in Z.\)
Vậy.....
(x-2)^20-(x-2)^18=0
(x-2)^18[(x-2)^2-1]=0
suy ra (x-2)^18=0;(x-2)^2-1=0
x-2=0 ;(x-2)^2=1 ;(x-2)^2=-1
x=2 ;x-2=1 ;x-2=-1
x=3 x=1
a)x3=125
x3=53
=>x=5
Vậy x=5
b)(x-1)3=27
(x-1)3=33
=>x-1=3
x=3+1
x=4
Vậy x=4
c)4x=16
4x=42
=>x=2
Vậy x=2
d)3x=81
3x=34
=>x=4
Vậy x=4
d)x5=32
x5=25
=>x=2
Vậy x=2
a) 3x+1 =279
=> 3x * 31 = (33)9 = 3 3 x 9 = 327
=> 3x = 327 : 31 = 326
=> 3x = 3 26
=> x= 26
b) ( x - 1 ) 5 = 32
=> ( x - 1 )5 = 25
=> x - 1 = 2
=> x = 2 + 1 = 3
c) 2 x = 815
=> 2x =( 24)15
=> 2x = 2 4 x 15 = 2 60
=> 2x = 260 => x=60
a, 2.3x = 18
=> 3x = 9 = 32
=> x = 2
b, 2x + 3.2x + 4.2x = 32
=> 2x.(1+3+4) = 32
=> 2x . 8 = 32
=> 2x = 4 = 22
=> x = 2
c, 3x + 4x = 5x
Câu này mik chưa nghĩ ra
a)1.3^x=18
=>3^x=18:2=9
=>3^x=3^2
=>x=2
b)=>2^x.(1+3+4)=32
=>2^x.8=32
=>2^x=4
=>2^x=2^2
=>x=2