Maths 對數

1. log 2/log_100 64
=log 2/[log 64/log100]
=2log 2/6log 2
=2/6
=1/3


2. [log 5^(2/7)][log_5 1000]
=[log 5^(2/7)][log 1000/log5]
=[(2/7)log 5][log 1000/log5]

=(2/7)log 1000
=(2/7)(3)
=6/7

1.
(log_y x^2)(log_x y^3)
=(2log x/log y)(3log y/log x)
=(2)(3)
=6

2.
log_x^(1/2) y^2 / 8log_x y
=[log y^2/log x^(1/2)] / [8log y/log x]
=[2log y/(1/2)log x] / [8log y/log x]
=[4log y/log x] [8log x/log y]
=(4)(8)
=32

2015-04-11 20:06:03 補充：
2.
log_x^(1/2) y^2 / 8log_x y
=[log y^2/log x^(1/2)] / [8log y/log x]
=[2log y/(1/2)log x] / [8log y/log x]
=[4log y/log x] [log x/8log y]
=(4)(1/8)
=1/2

1
[log (8^1/3)]/(log 64/log 100)
=(1/3)log 8 /(log 64 /log 100)
=(1/3)log 8 /(2 log 8 /2)
=1/3

2
[log 5^(2/7)](log 1000)/(log 5)
=(2/7)(3)
=6/7

1.
[(log x^2)/(log y)][(logy^3)/(log x)]
=(2)(3)
=6

2.
[(log y^2)/(0.5 log x)]/[(8 log y)/log x]
=4/8
=0.5

2015-04-11 14:39:23 補充：
To Lam Tsun Wai：
我認為你在第二個第二題是做錯了，因為8是跟log y不是log x