BenoguigoliB

2021-09-11

Solve the equation

$9}^{\left({x}^{2}\right)}={3}^{3x+2$

Alannej

Skilled2021-09-12Added 104 answers

Step 1

The given equation is$9}^{\left({x}^{2}\right)}={3}^{3x+2$ . This equation is with a single variable x.

Any equation of the form$a{x}^{2}+bx+c$ 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

$9}^{\left({x}^{2}\right)}={3}^{3x+2$

$\mathrm{log}\left({9}^{{x}^{2}}\right)=\mathrm{log}\left({3}^{3x+2}\right)$ (taking $\mathrm{log}$ on both sides)

${x}^{2}\mathrm{log}\left(9\right)=(3x+2)\mathrm{log}\left(3\right)\text{}\text{}\text{}\left({\mathrm{log}b}^{a}=a\mathrm{log}b\right)$

${x}^{2}\mathrm{log}\left({3}^{2}\right)=(3x+2)\mathrm{log}\left(3\right)$

$({x}^{2}\times 2)\mathrm{log}\left(3\right)=(3x+2)\mathrm{log}\left(3\right)\text{}\text{}\text{}\left({\mathrm{log}b}^{a}=a\mathrm{log}b\right)$

$2{x}^{2}=3x+2$ ...(1)

Equation (1) is a quadratic equation. Solving a quadratic equation will give 2 roots.

Step 3

Solve equation (1) for x

$2{x}^{2}-3x-2=0$

$2{x}^{2}-4x+x-2=0$

2x(x-2)+1(x-2)=0

(2x+1)(x-2)=0

$x=2,-\frac{1}{2}$

Therefore, value of x is 2 and$-\frac{1}{2}$

The given equation is

Any equation of the form

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

Equation (1) is a quadratic equation. Solving a quadratic equation will give 2 roots.

Step 3

Solve equation (1) for x

2x(x-2)+1(x-2)=0

(2x+1)(x-2)=0

Therefore, value of x is 2 and

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