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6 tháng 10 2021

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6 tháng 10 2021

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23 tháng 8 2023

a) \(4^n=4096\Rightarrow4^n=4^6\Rightarrow n=6\)

b) \(5^n=15625\Rightarrow5^n=5^6\Rightarrow n=6\)

c) \(6^{n+3}=216\Rightarrow6^{n+3}=6^3\Rightarrow n+3=3\Rightarrow n=0\)

d) \(x^2=x^3\Rightarrow x^3-x^2=0\Rightarrow x^2\left(x-1\right)=0\Rightarrow\left[{}\begin{matrix}x=0\\x-1=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

e) \(3^{x-1}=27\Rightarrow3^{x-1}=3^3\Rightarrow x-1=3\Rightarrow x=4\)

f) \(3^{x+1}=9\Rightarrow3^{x+1}=3^2\Rightarrow x+1=2\Rightarrow x=1\)

g) \(6^{x+1}=36\Rightarrow6^{x+1}=6^2\Rightarrow x+1=2\Rightarrow x=1\)

h) \(3^{2x+1}=27\Rightarrow3^{2x+1}=3^3\Rightarrow2x+1=3\Rightarrow2x=2\Rightarrow x=1\)

i) \(x^{50}=x\Rightarrow x^{50}-x=0\Rightarrow x\left(x^{49}-1\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x^{49}-1=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=0\\x^{49}=1=1^{49}\end{matrix}\right.\)  \(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

23 tháng 8 2023

4n  =  4096 

4n = 212

n = 12

5n = 15625 

5n = 56

n   = 6

6n+3 = 216

6n+3 = 23.33

6n+3 = 63

n + 3 = 3

 

 

31 tháng 3 2022

gfvfvfvfvfvfvfv555

17 tháng 10 2022

dễ

5 tháng 9 2019

b. 1404 : [118 - (4x + 6)] = 27

118 - (4x + 6) = 52

4x + 6 = 66

4x = 60

x = 15

5 tháng 9 2019

d) \(5x^2-3x=0\)

\(\Leftrightarrow x\left(5x-3\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\5x-3=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=0\\x=\frac{3}{5}\end{cases}}\)

e) \(3\left(x-1\right)+4\left(x-1\right)^2=0\)

\(\Leftrightarrow\left(x-1\right)\left[3-4.\left(x-1\right)\right]=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-1=0\\3-4\left(x-1\right)=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=1\\4\left(x-1\right)=3\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=1\\x-1=\frac{3}{4}\Rightarrow x=\frac{7}{4}\end{cases}}\)

f) \(2\left(x-2\right)^2=\left(x-2\right)\)

\(\Leftrightarrow\orbr{\begin{cases}x-2=0\\2\left(x-2\right)-1=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=2\\x-2=\frac{1}{2}\Rightarrow x=\frac{5}{2}\end{cases}}\)

g) \(\left(x-2020\right)^4=\left(x-2020\right)^2\)

\(\Leftrightarrow\orbr{\begin{cases}\left(x-2020\right)^2=0\\\left(x-2020\right)^2-1=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=2020\\x=2019,x=2021\end{cases}}\)

27 tháng 8 2023

Bài 1 :

\(M=\dfrac{30-2^{20}}{2^{18}}=\dfrac{2.15-2^{20}}{2^{18}}=\dfrac{15}{2^{17}}-2^2=\dfrac{15}{2^{17}}-4< 0\left(\dfrac{15}{2^{17}}< 1\right)\)

\(N=\dfrac{3^5}{1^{2021}+2^3}=\dfrac{3^5}{9}=\dfrac{3^5}{3^2}=3^3=27\)

\(\Rightarrow M< N\)

27 tháng 8 2023

Bài 3 :

a) \(t^2+5t-8\) khi \(t=2\)

\(=5^2+2.5-8\)

\(=25+10-8\)

\(=27\)

b) \(\left(a+b\right)^2-\left(b-a\right)^3+2021\left(1\right)\)

\(\left\{{}\begin{matrix}a=5\\b=a+1=6\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}a+b=11\\b-a=1\end{matrix}\right.\)

\(\left(1\right)=11^2-1^3+2021=121-1+2021=2141\)

c) \(x^3-3x^2y+3xy^2-y^3=\left(x-y\right)^3\left(1\right)\)

\(\left\{{}\begin{matrix}x=3\\y=2\end{matrix}\right.\) \(\Rightarrow x-y=1\)

\(\left(1\right)=1^3=1\)

= 52+9.4
= 25+36
= 61

làm wen ko ?<:

6 tháng 4 2022

\(14.7^{2021}=35.7^{2021}-3.49^x\)

\(\Leftrightarrow2.7^{2022}=5.7^{2022}-3.7^{2x}\)

\(\Leftrightarrow3.7^{2x}=3.7^{2022}\) \(\Leftrightarrow7^{2x}=7^{2022}\)

\(\Leftrightarrow2x=2022\Leftrightarrow x=1011\) (TM \(x\in Z\))

Vậy \(x=1011\)

5 tháng 8 2023

mn ơi giúp mình với thanh kiu nhìu

5 tháng 8 2023

Để olm giúp em nhá

(9989)69 = 996141 = (992)3070.99 = (\(\overline{..01}\))3070.99 = \(\overline{..99}\)

62021 = (65)404.6 = 7776404.6 = \(\overline{...76}.6\) = \(\overline{...56}\)

A=142022.162022=(14.16)2022=2242022= (2242)1001\(\overline{...76}\)1001=\(\overline{...76}\)