Solve 5-ln(x-4)=ln3

Evaluate

5 - ln (x - 4) = ln (3)

Find the domain

More Steps

5 - ln (x - 4) = ln (3), x > 4

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

- ln (x - 4) = ln (3) - 5

Evaluate the logarithm

More Steps

- ln (x - 4) = ln (\frac{3}{e ^{5}})

Simplify

ln (x - 4) = - ln (\frac{3}{e ^{5}})

Rewrite the logarithm

ln (x - 4) = ln (\frac{e ^{5}}{3})

Rewrite the expression

x - 4 = \frac{e ^{5}}{3}

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

x = \frac{e ^{5}}{3} + 4

Add the numbers

More Steps

x = \frac{e ^{5} + 12}{3}

Check if the solution is in the defined range

x = \frac{e ^{5} + 12}{3}, x > 4

Solution

x = \frac{e ^{5} + 12}{3}

Alternative Form

x \approx 53.471053

Solve the equation