I have been trying to solve it for a few days for my nephew but I am not able to remember what I learned back in school 15 years ago, please any help is appreciated

ln(2x-1) + (ln(2x-1)^2 = 4

And also, can you please confirm if the following one is correct?

log(x^2 - 9x) - logx = 2

log (x^2-9x / x) = 2

log (x-9) = 2

x-9 = 100

x = 109

Thank you in advanced!