[數學]10^a=2及10^b=3

已知10^a=2，10^b=3
a) 求100^a *1000^b的值。
10^a=2=>a=log2
10^b=3=>b=log3
100^a*1000^b
=[(10^2)^a]*[(10^3)^b]
=[(10^a)^2]*[(10^b)^3]
=4*27
=108
b) 求 a log4_10+blog9_10的值。
alog4_10+blog9_10
=a/log4+b/log9
=log2/log4+log3/log9
=1
c) 以a及b表示下列各數:
(i) log√12
=(1/2)log12
=(1/2)*(2log2+log3)
=(1/2)*(2a+b)
=(2a+b)/2
(ii) log240
=3log2+log3+log10
=3a+b+1
(iii) log45
=log5+2log3
=1－a+2b

a>a=56 b=0.5a>a=56 b=0.5a>a=56 b=0.5a>a=56 b=0.5a>a=56 b=0.5a>a=56 b=0.5a>a=56 b=0.5