Question 1201721: ln(x^2-9x+8)=ln(18-6x) ,x in Real Numbers
I got two solutions, x=-2 and x=5
Graphically, x=-2 seems to be the only solution.
Why is x=5 not a solution? Please explain. Thank you.
Answer by ikleyn(52908)   (Show Source):
You can put this solution on YOUR website! .
The number 5 definitely is not the solution, because x^2-9x+8 is then
5^2 -9*5+8 = -12,
negative number, while the argument under the logarithm must be positive and can not be negative.
When you solve logarithmic equation and find the potential solution (potential roots),
it is a necessary part of work to check if the expressions under all participating logarithmic functions
in the original equation are positive.
If at least one such expression under logarithm function is not positive,
such potential roots are ERRONEUS and are rejected.
Solved, answered and explained.
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On solving logarithmic equations, see my lesson
- Solving logarithmic equations
in this site (free of charge, as everything in this site).
You will find there many similar problems solved with complete explanations, your templates, to learn from.
It is like having your home teacher sit next to you and patiently explain
each step to you, repeating this as many times as needed, at the free of charge basis.
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