ln(x+19)=ln(7x-8) Solve the equation. Check for extraneous solutions.

To evaluate the equation ln(x+19)=ln(7x-8) , we apply natural logarithm property: e^(ln(x))=x .
Raise both sides by base of e .
e^(ln(x+19))=e^(ln(7x-8))
x+19=7x-8
Subtract 7x from both sides of the equation.
x+19-7x=7x-8-7x
-6x+19=-8
Subtract 19 from both sides of the equation.
-6x+19-19=-8-19
-6x=-27
Divide both sides by -6 .
(-6x)/(-6)=(-27)/(-6)
x=9/2
Checking: Plug-in x=9/2 on ln(x+19)=ln(7x-8) .
ln(9/2+19)=?ln(7*9/2-8)
ln(9/2+38/2)=?ln(63/2-16/2)
ln(47/2)=ln(47/2)      TRUE
Thus, the x=9/2 is the real exact solution of the equation ln(x+19)=ln(7x-8) .  There is no extraneous solution.