a) \(3^{2x-1}=243\)

\(\Leftrightarrow3^{2x-1}=3^5\)

\(\Leftrightarrow2x-1=5\)

\(\Leftrightarrow2x=5+1\)

\(\Leftrightarrow2x=6\)

\(\Leftrightarrow x=\dfrac{6}{2}\)

\(\Leftrightarrow x=3\)

Vậy \(x=3\)

b) \(\left(3^x\right)^2:3^3=\dfrac{1}{243}\)

\(\Leftrightarrow3^{2x}:3^3=\dfrac{1}{3^5}\)

\(\Leftrightarrow3^{2x}:3^3=3^{-5}\)

\(\Leftrightarrow3^{2x-3}=3^{-5}\)

\(\Leftrightarrow2x-3=-5\)

\(\Leftrightarrow2x=-5+3\)

\(\Leftrightarrow2x=-2\)

\(\Leftrightarrow x=-\dfrac{2}{2}\)

\(\Leftrightarrow x=1\)

Vậy \(x=1\)

c) \(2^{3x+2}=4^{x+5}\)

\(\Leftrightarrow2^{3x+2}=\left(2^2\right)^{x+5}\)

\(\Leftrightarrow2^{3x+2}=2^{2\left(x+5\right)}\)

\(\Leftrightarrow3x+2=2\left(x+5\right)\)

\(\Leftrightarrow3x+2=2x+10\)

\(\Leftrightarrow3x-2x=10-2\)

\(\Leftrightarrow x=8\)

Vậy \(x=8\)

d) \(3^{x+1}=9^x\)

\(\Leftrightarrow3^{x+1}=\left(3^2\right)^x\)

\(\Leftrightarrow3^{x+1}=3^{2x}\)

\(\Leftrightarrow x+1=2x\)

\(\Leftrightarrow2x-x=1\)

\(\Leftrightarrow x=1\)

Vậy \(x=1\)

a) 2^x = 16   b) 3^{x + 1} = 9^x

2^x = 2⁴            3^{x + 1} = 3^2x

x = 4                 x + 1 = 2x

                         x      = 1

c) 2^{3x + 2} = 4^{x + 2}

2^{3x + 2} = 2^{2(x + 2)}

3x + 2 = 2(x + 2)

3x + 2 = 2x + 4

x         = 2

d) 3^{2x - 1} = 243

3^{2x - 1} = 3⁵

2x - 1 = 5

2x = 6

x = 3

a)3^x+1=9^x

3^x+1=3.3^x

3^x+1=3^x+1

=>x thuộc TH Z

b)2^3.x+2=4^x+5

2^3x+2=2^2.(x+5)

2^3x+2=2^2x+10

2^3x=2^2x+8

3x-2x=8

=>x=8

c)3^2x-1=243

3^2x=243.3

3^2x=729

3^2x=3^6

=>2x=6

x=6:2=3

chúc bạn học tốt nha

thank you

óc chó

\(a,\left(0,3\right)^{x-3}=1\\ \Leftrightarrow x-3=0\\ \Leftrightarrow x=3\\ b,5^{3x-2}=25\\ \Leftrightarrow3x-2=2\\ \Leftrightarrow3x=4\\ \Leftrightarrow x=\dfrac{4}{3}\\ c,9^{x-2}=243^{x+1}\\ \Leftrightarrow3^{2x-4}=3^{5x+5}\\ \Leftrightarrow2x-4=5x+5\\ \Leftrightarrow3x=-9\\ \Leftrightarrow x=-3\)

d, Điều kiện: \(x>-1;x\ne0\)

\(log_{\dfrac{1}{x}}\left(x+1\right)=-3\\ \Leftrightarrow x+1=x^3\\ x\simeq1,325\left(tm\right)\)

e, Điều kiện: \(x>\dfrac{5}{3}\)

\(log_5\left(3x-5\right)=log_5\left(2x+1\right)\\ \Leftrightarrow3x-5=2x+1\\ \Leftrightarrow x=6\left(tm\right)\)

f, Điều kiện: \(x>\dfrac{1}{2}\)

\(log_{\dfrac{1}{7}}\left(x+9\right)=log_{\dfrac{1}{7}}\left(2x-1\right)\\ \Leftrightarrow x+9=2x-1\\ \Leftrightarrow x=10\left(tm\right)\)

Mình cần gấp ạ ! * cảm ơn

b) \(3^{x+1}=9^x\)

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

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

\(\Rightarrow x+1=2x\)

\(1=2x-x\)

\(1=x\)

Vậy x=1

c) 2^3x+2 = 4^x+5                                                                  d)3^2x-1 = 243

   2^3x+2 = (2²)^x+5                                                                3^2x-1 = 3⁵

   2^3x+2 = 2^2x+10                                               => 2x-1 = 5

=> 3x+2 = 2x + 10                                                 2x = 6

   3x - 2x = 10-2                                                    x=3

    => x = 8

a

\(\Rightarrow\)\(2^x=16\)

\(\Rightarrow\) \(2^4\)

b) \(3^{x+1}=9^x=3^{2x}\)

\(\Rightarrow x+1=2x\Leftrightarrow x=1\)

c) \(2^{3x+2}=4^x+5\Leftrightarrow4^{2x+1}=4^{x+5}\)

\(\Rightarrow2x+1=x+5\)\(\Rightarrow x=4\)

d) \(3^{2x-1}=243=3^5\)

\(\Rightarrow2x-1=5\Rightarrow x=3\)

a) \(2^x=16\)

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

\(\Rightarrow x=4\)

Vậy \(x=4.\)

b) \(3^{x+1}=9^x\)

d) \(3^{2x-1}=243\)

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

\(\Rightarrow2x-1=5\)

\(\Rightarrow2x=5+1\)

\(\Rightarrow2x=6\)

\(\Rightarrow x=6:2\)

\(\Rightarrow x=3\)

Vậy \(x=3.\)

Chúc bạn học tốt!

a, 2³ + 2 = 4^x + 5

8 + 2 = 4^x + 5

10 = 4^x + 5

=> 4^x = 5

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