Use the one-to-one property of logarithms to solve

Question

Question. . log₉ (2n² − 14n)= log₉ (−45 + n² )

=2n²-14n = -45 + n²

=2n²-n²-14n+45=0

=n²-14n+45=0

=(n-5)(n-9) = 0

=n-5=0 or n-9=0

=n-5=0 or n-9=0

=n = 5 or n= 9

Is this correct up to here?

and then, what is the final answer and how to solve this question?

I don't know the next step.

Answer 1

It is correct but you need to take into consideration that all inputs of logarithmic functions must be positive. Hence, n=5 is not allowed because -45+25<0 and so the only solution is n=9.