PLZZ/\/\"

化簡下列各數式。
(a) (-27a^6)^2/3 /(16a^-4)^3/4

Ans:[(-3)^3*(2/3) a^6*(2/3)]/[(2^4*3/4)a^-4*3/4]
=(-3^2 a^4)/(2^3 a^-3)
=9a^7/8//

設 log 2=a , log3= b , log7= c。把下列各數以 a, b和c表示。
(a) log 42=log 7*3*2=log 7+log 3+log2=a+b+c//
(b) log 105=log(7 * 5 *3)=log 7+log5+log3=c+b+log5//
(c) log 375=log(5^3 x 3)=3log5 +log3=3log5+b//
(d) log 開方60=log(60^1/2)=1/2(log 6*2*5)=1/2(log4 +log 3+log5)=1/2(2a+b+log5)//
(e) log 6開方42=log6 +log √42=log(3*2)+0.5log(7*3*2)=a+b+0.5c+0.5a+0.5b=1.5a+1.5b+0.5c//
(f) log [sin 3.14/3]log (sin 180/3)=log(√3/2)=log√3-log2=0.5log3-log2=0.5b-a//


求以下各式的值。
(a) log8 + log375 - log3=log(375 x 8 /3)=log 100= 3//
(b) log16/log2=log2^4/log2=4log2/log2=4//
(c) log125 - log5 / log5開方5=log(125/5)/0.5log125=5/0.5log125=10/log125//
(d) logx^2 - log 開方x /log 3開方x =(2logx-0.5logx)/(log3+0.5logx)=1.5logx/(log3+0.5logx)