To solve, express left side as one logarithm. To do so, apply the quotient property which is ln M - ln N = ln(M/N).
Since both sides of the equation have the same base of logarithm, to solve for x set the arguments of ln equal to each other.
`(x-4)/(x+1) = 6`
Then, multiply both sides by x+1 to simplify the equation.
Then, bring together the terms with x on one side of the equation. To do so, subtract both sides by x.
Also, bring together the terms without x on one side of the equation. So, subtract both sides by 6.
And divide both sides by 5.
Hence, the solution is x=-2.
`ln(x -4) - ln(x +1) = ln6`
passing to the exponent
Now multiply both side by (x +1)
`x-4= 6x + 6`
adding both sides 4:
`x -4 + 4 = 6x + 6 +4`
`x = 6x+ 10`
subtracting now both sides 6x:
`x - 6x = 6x - 6x + 10`