求解答3條數學題

(1)

Let x = ln a and y = ln b
then a = e^x and b = e^y

ln (a/b) = ln (e^x/e^y) = ln e^(x-y) = (x-y) ln e = x - y = ln a - ln b


(2)

log(x-1) + log(x+1) = 2log(x+2)
log[(x-1)(x+1)] = log(x+2)^2
x^2 - 1 = (x+2)^2
x^2 - 1 = x^2 + 4x + 4
x = -5/4 (rejected)

therefore, there are no real solutions


(3)

x^6 - 9x^3 + 8 >0
(x^3 - 1)(x^3 - 8) >0
x^3 < 1 or x^3 > 8
x < 1 or x > 2

第一題題目錯誤...............