What is the answer to (3^x+2)^2=121 ?

The answer to (3^x+2)^2=121 is x=2

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(3^x+2)^2=121

(3^{x} + 2)^{2} = 121

x = 2

Solution steps

(3^{x} + 2)^{2} = 121

Rewrite the equation with

3^{x} = u

(u + 2)^{2} = 121

Solve

(u + 2)^{2} = 121 : u = 9, u = - 13

u = 9, u = - 13

Substitute back

u = 3^{x},

solve for

x

Solve

3^{x} = 9 : x = 2

Solve

3^{x} = - 13 :

No Solution for

x \in R

x = 2

2^{x} = 2

3^{1 - 2 x} = e^{2 l n (3)}

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

2^{x^{2} - 2 x} = 8

e^{x^{2}} = 0