solve logarithmic equation in exact form only. show work.

Question

log_5(x-3)+ log_5(x-6)-log_5(x+1)=2

Answer 1

log_5 [(x-3)(x-6)/(x+1) = 2 , we know x > 6

(x-3)(x-6)/(x+1) = 5^2
x^2 - 9x + 18 = 25x + 25
x^2 - 34x - 7 = 0

x = (34 ± √1184)/2
= (34 ± 4√74)/2
= 17 ± 2√74 , but x > 6

x = 17 + 2√74

Answer 2

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