Solve 3e^(2x^4)=4

Evaluate

3 e^{2 x^{4}} = 4

Divide both sides

\frac{3 e ^{2 x^{4}}}{3} = \frac{4}{3}

Divide the numbers

e^{2 x^{4}} = \frac{4}{3}

Take the logarithm of both sides

ln (e^{2 x^{4}}) = ln (\frac{4}{3})

Evaluate the logarithm

2 x^{4} = ln (\frac{4}{3})

Divide both sides

\frac{2 x ^{4}}{2} = \frac{ln ( \frac{4}{3} )}{2}

Divide the numbers

x^{4} = \frac{ln ( \frac{4}{3} )}{2}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 4 \frac{ln ( \frac{4}{3} )}{2}

Simplify the expression

More Steps

x = \pm \frac{4 8 ln ( \frac{4}{3} )}{2}

Separate the equation into 2 possible cases

x = \frac{4 8 ln ( \frac{4}{3} )}{2} x = - \frac{4 8 ln ( \frac{4}{3} )}{2}

Solution

x_{1} = - \frac{4 8 ln ( \frac{4}{3} )}{2}, x_{2} = \frac{4 8 ln ( \frac{4}{3} )}{2}

Alternative Form

x_{1} \approx - 0.615844, x_{2} \approx 0.615844

Solve the equation