Solve ln(5-2x)=-7

Evaluate

ln (5 - 2 x) = - 7

Find the domain

More Steps

ln (5 - 2 x) = - 7, 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^{- 7}

Evaluate the power

5 - 2 x = \frac{1}{e ^{7}}

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

- 2 x = \frac{1}{e ^{7}} - 5

Subtract the numbers

More Steps

- 2 x = \frac{1 - 5 e ^{7}}{e ^{7}}

Change the signs on both sides of the equation

2 x = \frac{5 e ^{7} - 1}{e ^{7}}

Multiply by the reciprocal

2 x \times \frac{1}{2} = \frac{5 e ^{7} - 1}{e ^{7}} \times \frac{1}{2}

Multiply

x = \frac{5 e ^{7} - 1}{e ^{7}} \times \frac{1}{2}

Multiply

More Steps

x = \frac{5 e ^{7} - 1}{2 e ^{7}}

Check if the solution is in the defined range

x = \frac{5 e ^{7} - 1}{2 e ^{7}}, x < \frac{5}{2}

Solution

x = \frac{5 e ^{7} - 1}{2 e ^{7}}

Alternative Form

x \approx 2.499544

Solve the equation