Solve ln(x 2)=−2

Evaluate

ln (x \times 2) = - 2

Find the domain

More Steps

ln (x \times 2) = - 2, x > 0

Use the commutative property to reorder the terms

ln (2 x) = - 2

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

2 x = e^{- 2}

Evaluate the power

2 x = \frac{1}{e ^{2}}

Multiply by the reciprocal

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

Multiply

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

Multiply

More Steps

x = \frac{1}{2 e ^{2}}

Check if the solution is in the defined range

x = \frac{1}{2 e ^{2}}, x > 0

Solution

x = \frac{1}{2 e ^{2}}

Alternative Form

x \approx 0.067668

Solve the equation