What is the answer to solvefor x,z=y^3e^{x^2} ?

The answer to solvefor x,z=y^3e^{x^2} is x=sqrt(ln(z)-3ln(y)),x=-sqrt(ln(z)-3ln(y))

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solvefor x,z=y^3e^{x^2}

solve for

x, z = y^{3} e^{x^{2}}

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

Solution steps

z = y^{3} e^{x^{2}}

Switch sides

y^{3} e^{x^{2}} = z

Divide both sides by

y^{3}

e^{x^{2}} = \frac{z}{y ^{3}}

Apply exponent rules

x^{2} = ln (\frac{z}{y ^{3}})

Solve

x^{2} = ln (\frac{z}{y ^{3}}) : x = ln (z) - 3 ln (y), x = - ln (z) - 3 ln (y)

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

3^{2 x - 1} - 3 x = 18

e^{- l n (x)} = 0.2

e^{x} = \frac{3}{2}

9^{x + 3} = 243

2^{5 x - 4} = 18

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