Solve 3ln(2x^3) = 2

Evaluate

3 ln (2 x^{3}) = 2

Find the domain

More Steps

3 ln (2 x^{3}) = 2, x > 0

Divide both sides

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

Divide the numbers

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

Convert the logarithm into exponential form using the fact that lo g_{a} x = b is equal to x = a^{b}

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

Use a^{\frac{m}{n}} = n a^{m} to transform the expression

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

Divide both sides

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

Divide the numbers

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

Take the 3 -th root on both sides of the equation

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

Calculate

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

Simplify the root

More Steps

x = \frac{9 64 e ^{2}}{2}

Check if the solution is in the defined range

x = \frac{9 64 e ^{2}}{2}, x > 0

Solution

x = \frac{9 64 e ^{2}}{2}

Alternative Form

x \approx 0.991212

Solve the equation