急 ! Logarithmic Function.

general equation: logab = c => a^c = b
such that you can derive by yourself: logab = log a / log b whatever the base is

22a.
log5 0.6 = log10 0.6 / log10 5
= log10 (3/5) / b
= (log10 3 - log10 5) / b
= (a-b)/b
22c.
log10 (2/27) = log10 (2) - log10 (27)
= log10 (10/5) - log10 (3^3)
= log10 (10) - log10 (5) - 3log10 (3)
= 1 - b - 3a

23a.
log x = 2 log y
log x = log (y^2)
x = y^2
23b.
log (xy) = 2
log (xy) = log 100
xy = 100 => x = 100/y
23c.
(1/2)log x = 2 + log y
log [x^(1/2)] = log 100 + log y
log [x^(1/2)] = log (100y)
x^(1/2) = 100y
x = 10000y^2
24d.
log4 (x-2y) = 3
log4 (x-2y) = 3 log4 (4)
log4 (x-2y) = log4 (4^3)
x-2y = 64
x = 64 + 2y

圖片參考：http://i41.tinypic.com/ux5bm.png


http://i41.tinypic.com/ux5bm.png

22(b)log(5)0.6
=log(10)0.6/log(10)5
=(log(10)3/5)/log(10)5
=(log(10)3-log(10)5)/log(10)5
=(a-b)/b
22(c)log(10)2/27
=log(10)2-log(10)27
=log(10)10/5-log(10)3^3
=1-log(10)5-3log(10)3
=1-b-3a
23(a)log x=2log y
log x=log y^2
x=y^2
23(b)log(xy)=2
xy=10^2
xy=100
x=100/y
(c)1/2log x=2+log y
log x=4+2log y
log x-2log y=4
log x-log y^2=4
log(x/y^2)=4
x/y^2=10^4
x/y^2=10000
x=10000y^2
(d)log(4)(x-2y)=3
x-2y=4^3
x-2y=64
x=2y+64
note:
the number in the brackets are the base of logarithmic functions