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5x=125
Mà: 53=125
=>x=3
32x=81
Mà: 34=81
=>32x=34
=>2x=4
=>x=4:2
=>x=2
52x-3-2.52=52.3
=>52x-3-50=75
=>52x-3=75+50
=>52x-3=125
Mà: 53=125
=> 52x-3=53
=>2x-3=3
=>2x=3+3
=>2x=6
=>x=6:2
=>x=3
5x=125
Mà: 53=125
=>x=3
32x=81
Mà: 34=81
=>32x=34
=>2x=4
=>x=4:2
=>x=2
52x-3-2.52=52.3
=>52x-3-50=75
=>52x-3=75+50
=>52x-3=125
Mà: 53=125
=> 52x-3=53
=>2x-3=3
=>2x=3+3
=>2x=6
=>x=6:2
=>x=3
a) 5x = 125
\(\Rightarrow\)5x = 53
\(\Rightarrow\)x = 3
b, 32x = 81
\(\Rightarrow\)32x = 34
\(\Rightarrow\)2x = 4
\(\Rightarrow\) x = 4 : 2
\(\Rightarrow\) x = 2
c, 52x-3 - 2 . 52 = 52 . 3
52x-3 - 2 . 25 = 25 . 3
52x-3 - 50 = 75
52x-3 = 75 + 50
52x-3 = 125
52x-3 = 53
2x - 3 = 3
2x = 3 + 3
2x = 6
x = 6 : 2
x = 3
a, 5x = 125 suy ra 5x = 53 suy ra x = 3
b, 32x = 81 suy ra 32x = 34 suy ra x = 2
c, 52x - 3 - 2.52 = 52 . 3
suy ra 52x : 53 = 52 .3 + 2. 52
suy ra 52x : 53 = 52 . 5
suy ra 52x = 53 . 52 . 53
52x = 56 suy ra 2x = 6 suy ra x = 3
\(A=1+7+7^2+7^3+...+7^{200}\)
\(\Rightarrow7A=7+7^2+7^3+...+7^{201}\)
\(\Rightarrow7A-A=\left(7+7^2+...+7^{201}\right)-\left(1+7+7^2+...+7^{200}\right)\)
\(\Rightarrow6A=7^{201}-1\)
\(\Rightarrow A=\frac{7^{201}-1}{6}\)
\(B=5^1+5^3+5^5+...+5^{101}\)
\(\Rightarrow5^2B=5^3+5^5+5^7+...+5^{103}\)
\(\Rightarrow25B-B=\left(5^3+5^5+...+5^{103}\right)-\left(5+5^3+...+5^{101}\right)\)
\(\Rightarrow24B=5^{103}-5\)
\(\Rightarrow B=\frac{5^{103}-5}{24}\)
\(D=1+a+a^2+a^3+...+a^n\)
\(\Rightarrow aD=a+a^2+a^3+...+a^{n+1}\)
\(\Rightarrow aD-D=\left(a+a^2+...+a^{n+1}\right)-\left(1+a+a^2+...+a^n\right)\)
\(\Rightarrow\left(a-1\right)D=a^{n+1}-1\)
\(\Rightarrow D=\frac{a^{n+1}-1}{a-1}\)
a)5x=125=53
=>x=3
b)32x=81=34
=>2x=4
x=4/2
x=2
c)52x-3-2*52=52*3
52x-3=52*3+2*52=52(3+2)=52*5
52x-3=53
=>2x-3=3
2x=3+3
2x=6
x=6/2
x=3
lần sau nếu ghi dẫu mũ như vậy thì bạn nhớ ngoặc vào
Ta có \(5^x=125\)
\(\Rightarrow5^x=5^3\Rightarrow x=3\)
Vậy x = 3
b,\(3^{2x}=81\)
\(\Rightarrow3^{2x}=3^4\Rightarrow2x=4\Rightarrow x=2\)
Vậy x = 2
c,\(5^{2x-3}-2.5^2=5^2.3\)
\(\Rightarrow5^{2x-3}=5^2.3+5^2.2\Rightarrow5^{2x-3}=5^2.\left(2+3\right)\Rightarrow5^{2x-3}=5^3\)
\(\Rightarrow2x-3=3\Rightarrow2x=6\Rightarrow x=3\)
Vậy x = 3
Ta có : \(\left(3-x\right)\left|x+5\right|=0\)
\(\Leftrightarrow\orbr{\begin{cases}3-x=0\\\left|x+5\right|=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=3\\x+5=0\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}x=3\\x=-5\end{cases}}\)
Ta có :
\(\left(3-x\right)\left|x+5\right|=0\)
\(\Rightarrow\orbr{\begin{cases}3-x=0\\\left|x+5\right|=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=3\\x+5=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=3\\x=-5\end{cases}}\)
(32)25.(33)4.(34)3=350.312.312=374
(52)50.(53)5=5115
(416)3.48.(42)4=
a 350 x312 x 312 = 374
b 5100 x 515 =5115
c 49 x 48 x 48 = 425
a,Vì |a|<5
=>|a|\(\in\){0,1,2,3,4}
=>a\(\in\){-4,-3,-2,-1,0,1,2,3,4}
=>-5<a<5\(\left(đpcm\right)\)
b,5x=125
=>5x=53
=>x=3
c,32x=81
=>(32)x=81
=>9x=81
=>9x=92
=>x=2
d,52x-3-2.52=52.3
=>52x:53-2.25=25.3
=>52x:53-50=75
=>52x:53=75+50
=>52x:53=125
=>52x=125.53
=>52x=53.53
=>52x=56
=>2x=6
=>x=3