Question

(3^2x+4)+1=2*(3^x+2) ; solve x

Answer 1

Step-by-step explanation:

Quadratic Equations

\begin{lgathered}{3}^{2x + 4} + 1 = 2 \times {3}^{x + 2} \\ ( {3}^{x + 2)2} + 1 = 2 \times {3}^{x + 2}\end{lgathered}32x+4+1=2×3x+2(3x+2)2+1=2×3x+2

=> A²+1 = 2A

=> A²-2A + 1 = 0

=>(A-1)²= 0

=> A = 1

=> 3^(x+2) = 3^0

=> x+2 = 0

=> x = -2

Therefore the value of x is -2

That's it

Hope it helped (+_+)

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Answer 2

Answer:

x=-2

Step-by-step explanation:

(3^2x+4)+1= 2.(3^x+2)

{(3^x+2)^2}+1-2.(3^x+2)=0. (a²+b²-2ab)

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

(3^x+2)=1

3^x×3^2=1

3^x=3^-2

Comparing powers because bases are same:-

x=-2