200分求解log函数,log(x−9)−log(8x−70)=log(1/x)log(x2+3)−log(x+2)=2+log(x−2)求2道题目,X值

Question

200分求解log函数,
log(x − 9) − log(8x − 70) = log(1/x)
log(x2 + 3) − log(x + 2) = 2 + log(x − 2)
求2道题目,X值

Answer 1

log(x − 9) − log(8x − 70) = log(1/x)
log(x-9)/(8x-70)=log(1/x)
所以有：(x-9)/(8x-70)=1/x
x^2-9x=8x-70
x^2-17x+70=0
(x-7)(x-10)=0
x=7 (舍去) 或 x=10
log(x2 + 3) − log(x + 2) = 2 + log(x − 2)
log(x2 + 3) − log(x + 2) -log(x − 2)=2
log(x^2+3)/(x+2)(x-2)=2
得：(x^2+3)/(x+2)(x-2)=100
x^2+3=100x^2-400
99x^2=403
x^2=403/99
x=-√403/99 (舍去) 或 x=√403/99