Question

Determine the exact solutions of the equation log_3(x^2+1)−log_3(x−1)=4

Answer 1

@Botev maybe if you just tell me how to approach it i can figure it out..? any ideas

Answer 2

\[\log_{3} (\frac{ x^ {2} + 1 }{ x - 1 }) = 4\]
Domain : \[x \gt 1\]
This leads to \[\frac{ x ^{2} + 1 }{ x - 1 } = 3^{4}\] which is a normal quadratic equation, just check the answers to fall in the Domain of the function.

Answer 3

okayyy thank you so much!!!

Answer 4

@Botev how does \[(x^2 +1)/(x-1) = 3^4\] get into a quadratic?

Answer 5

Multiply both sides by (x-1)