What is the answer to |3e^{z^2}|=9 ?

The answer to |3e^{z^2}|=9 is z=sqrt(ln(3)),z=-sqrt(ln(3))

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|3e^{z^2}|=9

3 e^{z^{2}} = 9

z = ln (3), z = - ln (3)

Decimal Notation

z = 1.04814 \dots, z = - 1.04814 \dots

Solution steps

3 e^{z^{2}} = 9

Rewrite the equation with

e^{z^{2}} = u

∣ 3 u ∣ = 9

Solve

∣ 3 u ∣ = 9 : u = - 3 or u = 3

u = - 3, u = 3

Substitute back

u = e^{z^{2}},

solve for

z

Solve

e^{z^{2}} = - 3 :

No Solution for

z \in R

Solve

e^{z^{2}} = 3 : z = ln (3), z = - ln (3)

z = ln (3), z = - ln (3)

(x - 2) (x + 8) \geq 0

\frac{12}{- 4}

36 x^{2} - 9 = 0

4 m + 1 \geq 9

x^{2} \geq 5

What is the answer to |3e^{z^2}|=9 ?
The answer to |3e^{z^2}|=9 is z=sqrt(ln(3)),z=-sqrt(ln(3))