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

Question

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

Answer 1

This is a different in natural logs.  Therefore, we can write this as a quotient.

 

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

 

 

The solution to a natural log is the exponent of the base number e.

 

e⁵ = (x - 4) / x

 

 

Multiply x on both sides of equation.

 

xe⁵ = x - 4

 

 

Subtract x on both sides of equation.

 

xe⁵ - x = -4

 

 

Factor out the x on the left side of equation.

 

x(e⁵ - 1) = -4

 

 

Divide both sides of equation by e⁵ - 1.

 

x = -4 / (e⁵ - 1)