nhanh ạ tôi cần gấp ạ

a) 2x = 16 <=>x=8

b) 3x+1 = 9x <=>9x-3x=1

<=>6x=1 <=>x=1/6

c) 23x+2 = 4x+5 <=>23x-4x=5-2

<=>19x=3 <=>x=3/19

d) 32x-1 = 243 <=>32x=244

<=>x=61/8

a/ 2x=16

x=8

b/ 3x+1=9x

3x-9x=-1

-6x=-1

x=1/6

c/ 23x+2=4x

23x-4x=-2

19x=-2

x=-2/19

d/ 32x-1=243

32x=244

x=61/8

+) Tính giá trị của  x² + 4x - 1 tại x = -2 + \(\sqrt{5}\)

=> (-2 + \(\sqrt{5}\)) ² + 4.(-2 + \(\sqrt{5}\)) - 1 = 4 - 4\(\sqrt{5}\) + 5 - 8 + 4\(\sqrt{5}\) - 1   = 0 

Vậy x² + 4x - 1  = 0 tại x = -2 + \(\sqrt{5}\)

+) A = 3x³.(x² + 4x  - 1 ) - 5x³ - 23x² - 7x + 1

       = 3x³.(x² + 4x  - 1 ) - 5x.(x² + 4x - 1) - 3x² - 12x + 1

      = (3x³ - 5x).(x² + 4x  - 1 ) - 3.(x² + 4x -1) - 2 =  (3x³ - 5x - 3).(x² + 4x  - 1 )  - 2

Vậy tại x = - 2 + \(\sqrt{5}\) thì A = - 2 

+) A =  (3x³ - 5x - 3).(x² + 4x  - 1 )  - 2 chia cho (x² + 4x  - 1 ) dư - 2

A:23x-18=14x

  23x-14x=18

9x          =18

x            =18:9

x             =2

Vậy ....

B:2^x+1 :16 = 8

2^x+1          =8x16

2^x+1          =128

2^x+1           =2⁷

x+1            =7

x               =7-1

x               =6 

Vậy ....

A

23x-18=14x

18=23x-14x

18=9x

2=x

B

2^x+1:16=8

2^x+1=128

2^x+1=2⁷

x+1=7

x=6

C

2^x+4x=20

2^x+4x=2³+4.3

x=3

Xin lỗi câu C tớ viết nhầm.Viết đúng là 2^x+4^x=20

23x+2=4x+5

\(\Rightarrow23x-4x=-2+5\)

\(\Rightarrow19x=3\)

\(\Rightarrow x=3:19=\dfrac{3}{19}\)

\(1,\\ a,2^x=16=2^4\Rightarrow x=4\\ b,3^{x+1}=9^x=3^{2x}\\ \Rightarrow x+1=2x\Rightarrow x=1\\ c,2^{3x+2}=4^{x+5}=2^{2\left(x+5\right)}\\ \Rightarrow3x+2=2x+10\Rightarrow x=8\\ d,3^{2x-1}=243=3^5\\ \Rightarrow2x-1=5\Rightarrow x=3\\ 2,\\ a,2^{225}=8^{75}< 9^{75}=3^{150}\\ b,2^{91}=\left(2^{13}\right)^7=8192^7>3125^7=\left(5^5\right)^7=5^{35}\\ c,99^{20}=\left(99^2\right)^{10}< \left(99\cdot101\right)^{10}=9999^{10}\\ 3,\\ a,12^8\cdot9^{12}=2^{16}\cdot3^8\cdot3^{24}=2^{16}\cdot3^{32}=\left(2\cdot3^2\right)^{16}=18^{16}\\ b,75^{20}=\left(3\cdot5^2\right)^{20}=3^{20}\cdot5^{40}=\left(3^{20}\cdot5^{10}\right)\cdot5^{30}=\left(3^2\cdot5\right)^{10}\cdot5^{30}=45^{10}\cdot5^{30}\)

Bài 1:

a) \(\Rightarrow2^x=2^4\Rightarrow x=4\)

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

c) \(\Rightarrow2^{3x+2}=2^{2x+10}\Rightarrow3x+2=2x+10\Rightarrow x=8\)

d) \(\Rightarrow3^{2x-1}=3^5\Rightarrow2x-1=5\Rightarrow x=3\)

Bài 2:

a) \(2^{225}=\left(2^3\right)^{75}=8^{75}< 9^{75}=\left(3^2\right)^{75}=3^{150}\)

b) \(2^{91}=\left(2^{13}\right)^7=8192^7>3125^7=\left(5^5\right)^7=5^{35}\)

c) \(99^{20}=\left(99^2\right)^{10}=9801^{10}< 9999^{10}\)

Bài 3:

a) \(12^8.9^{12}=\left(4.3\right)^8.9^{12}=4^8.3^8.9^{12}=2^{16}.9^4.9^{12}=2^{16}.9^{16}=\left(2.9\right)^{16}=18^{16}\)

b) \(75^{20}=\left(75^2\right)^{10}=5625^{10}=\left(45.125\right)^{10}=45^{10}.125^{10}=45^{10}.5^{30}\)

a, đk : x khác 5;-6 

\(x^2+12x+36+x^2-10x+25=2x^2+23x+61\)

\(\Leftrightarrow2x+61=23x+61\Leftrightarrow21x=0\Leftrightarrow x=0\)(tm) 

b, đk : x khác 1;3 

\(x^2+2x-15=x^2-1-8\Leftrightarrow2x-15=-9\Leftrightarrow x=3\left(ktmđk\right)\)

pt vô nghiệm 

a, đk : x khác 5;-6 

(tm) 

b, đk : x khác 1;3 

x2+2x−15=x2−1−8⇔2x−15=−9⇔x=3(ktmđk)x2+2x−15=x2−1−8⇔2x−15=−9⇔x=3(ktmđk)

pt vô nghiệm 

a: \(\Leftrightarrow\left(x+6\right)^2+\left(x-5\right)^2=2x^2+23x+61\)

\(\Leftrightarrow x^2+12x+36+x^2-10x+25=2x^2+23x+61\)

=>x=0(nhận)

b: \(\Leftrightarrow\left(x+5\right)\left(x-3\right)=\left(x+1\right)\left(x-1\right)-8\)

\(\Leftrightarrow x^2+2x-15=x^2-1-8\)

=>2x-15=-9

=>2x=-6

hay x=-3(nhận)

a, =2x²-3x+5

b,=x²-2x-5

c,2x²-19x+93(dư 368x-88)

b) \(x^3-5x^2+4x-20=0\)

\(=\left(x^3-5x^2\right)+\left(4x-20\right)=0\)

\(=x^2\left(x-5\right)+4\left(x-5\right)=0\)

\(=\left(x^2+4\right)\left(x-5\right)=0\)

\(x^2\ge0\)

\(\Rightarrow x^2+4\ge4>0\)

\(\Rightarrow x-5=0\)

\(\Rightarrow x=5\)