`ln(x + 1) - ln(x - 2) = ln(x)` Solve the logarithmic equation algebraically. Approximate the result to three decimal places.

loves2learn | Student

Condense the equation using properties of logs

`ln((x+1)/(x-2))=lnx `

Since there are ln's on both sides, set the inner parts equal to each other

`(x+1)/(x-2)=x`

Cross multiply and simplify,

`x^2-3x-1=0 `

Use the quadratic formula,

x=` (3+sqrt13)/2 = 3.303`

Note that I omitted the negative value because it is never an answer (you cannot take the log or ln of it).