Solve -7 ln(2x)=4

Evaluate

- 7 ln (2 x) = 4

Find the domain

More Steps

- 7 ln (2 x) = 4, x > 0

Change the sign

7 ln (2 x) = - 4

Divide both sides

\frac{7 ln ( 2 x )}{7} = \frac{- 4}{7}

Divide the numbers

ln (2 x) = \frac{- 4}{7}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

ln (2 x) = - \frac{4}{7}

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

2 x = e^{- \frac{4}{7}}

Evaluate the power

More Steps

2 x = \frac{7 e ^{3}}{e}

Multiply by the reciprocal

2 x \times \frac{1}{2} = \frac{7 e ^{3}}{e} \times \frac{1}{2}

Multiply

x = \frac{7 e ^{3}}{e} \times \frac{1}{2}

Multiply

More Steps

x = \frac{7 e ^{3}}{2 e}

Check if the solution is in the defined range

x = \frac{7 e ^{3}}{2 e}, x > 0

Solution

x = \frac{7 e ^{3}}{2 e}

Alternative Form

x \approx 0.282359

Solve the equation