Question

3^{2x+1}-12(3^x)+9=0

find x​

Answer 1

x = {0; 1}

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Given equation:

• 
  `3^(2x+1)-12(3^x)+9=0`

Rewrite it as:

• 
  `3*(3^(2x))-12(3^x)+9=0`

Divide all terms by 3:

• 
  `(3^(2x))-4(3^x)+3=0`

Factorize it as below:

• 
  `(3^(2x))-(3^x)-3(3^x)+3=0`

• 
  `3^(x)(3^x-1)-3(3^x-1)=0`

• 
  `(3^(x)-3)(3^x-1)=0`

Equate each factor to zero and solve each one:

• 
  `3^x-3=0\ > > \ 3^x=3\ > > \ 3^x=3^1\ > > \ \ x=1`

• 
  `3^x-1=0\ > > \ 3^x=1\ > > \ 3^x=3^0\ > > \ \ x=0`