高職數學 4-4 對數函數及圖形?

(1) 解方程式log(x+√6)+log(x－√6)=1
Sol
log(x+√6)+log(x－√6)=1
log[(x+√6)(x－√6)]=log10
log(x^2－6)=log10
x^2－6=10
x^2－16=0
(x+4)(x－4)=0
x=4 or x=－4(不合)
(2) 解方程式log2_x=logx_2
Sol
log2_x=logx_2
logx/log2=log2/logx
(logx)^2=(log2)^2
Set y=logx
y^2=(log2)^2
y=log2 or y=-log2
logx=log2 or logx=-log2
x=2 or x=1/2
(3) 已知log5_(3x－1)<3，試求x的範圍
Sol
log5_(3x－1)<3
log(3x－1)/log5<3
log(3x－1)/3log5
log(3x－1)<log125
3x－1<125
3x<126
x<42