Question

一道关于数学对数的题目。

(1) 已知3^a=2，用a表示log3^4-log3^6
（2）已知log3^2=a，3^b=5，用a、b表示log3^根号30

Answer 1

(1)3^a=2
a=log3(2)=lg2/lg3
lg2=alg3
log3^4-log3^6
=lg4/lg3-lg6/lg3
=(lg4-lg6)/迅袜lg3
=lg(4/袭乱6)/lg3
=lg(2/3)/lg3
=(lg2-lg3)/lg3
=(alg3-lg3)/lg3
=a-1

(2）log3^2=a=lg3/lg2
lg3=alg2
3^b=5
lg3^b=lg5
lg5=blg3=ablg2
log3^根号30
=lg根号30/拍昌档lg3
=1/2*lg30/lg3
=(1/2)*lg(2*3*5)/lg3
=(1/2)*(lg2+lg3+lg5)/lg3
=(1/2)*(lg2+alg2+ablg2)/alg2
=(1+a+ab)/(2a)

Answer 2

30