Solve \ln(5-2x)=-5

Evaluate

ln (5 - 2 x) = - 5

Find the domain

More Steps

ln (5 - 2 x) = - 5, x < \frac{5}{2}

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

5 - 2 x = e^{- 5}

Evaluate the power

5 - 2 x = \frac{1}{e ^{5}}

Move the constant to the right-hand side and change its sign

- 2 x = \frac{1}{e ^{5}} - 5

Subtract the numbers

More Steps

- 2 x = \frac{1 - 5 e ^{5}}{e ^{5}}

Change the signs on both sides of the equation

2 x = \frac{5 e ^{5} - 1}{e ^{5}}

Multiply by the reciprocal

2 x \times \frac{1}{2} = \frac{5 e ^{5} - 1}{e ^{5}} \times \frac{1}{2}

Multiply

x = \frac{5 e ^{5} - 1}{e ^{5}} \times \frac{1}{2}

Multiply

More Steps

x = \frac{5 e ^{5} - 1}{2 e ^{5}}

Check if the solution is in the defined range

x = \frac{5 e ^{5} - 1}{2 e ^{5}}, x < \frac{5}{2}

Solution

x = \frac{5 e ^{5} - 1}{2 e ^{5}}

Alternative Form

x \approx 2.496631

Solve the equation