Solve the equation 9^{(x^{2})}=3^{3x+2}

BenoguigoliB

BenoguigoliB

Answered question

2021-09-11

Solve the equation
9(x2)=33x+2

Answer & Explanation

Alannej

Alannej

Skilled2021-09-12Added 104 answers

Step 1
The given equation is 9(x2)=33x+2. This equation is with a single variable x.
Any equation of the form ax2+bx+c is a quadratic equation
The quadratic equation will have two solutions, hence there will be two values of x.
Step 2
Solve the given equation to get a quadratic equation
9(x2)=33x+2
log(9x2)=log(33x+2) (taking log on both sides)
x2log(9)=(3x+2)log(3)   (logba=alogb)
x2log(32)=(3x+2)log(3)
(x2×2)log(3)=(3x+2)log(3)   (logba=alogb)
2x2=3x+2...(1)
Equation (1) is a quadratic equation. Solving a quadratic equation will give 2 roots.
Step 3
Solve equation (1) for x
2x23x2=0
2x24x+x2=0
2x(x-2)+1(x-2)=0
(2x+1)(x-2)=0
x=2,12
Therefore, value of x is 2 and 12

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