若24^a=12,则log以24为底3的对数
问题描述:
若24^a=12,则log以24为底3的对数
答
a=log(24)12
=1/(log(12)24)
=1/(log(12)12+log(12)2)
=1/(1+1/log(2)12)
=1/(1+1/(2+log(2)3))
得到log(2)3=(3a-2)/(1-a)
所以
log(24)3
=log(24)12-log(24)4
=a-1/(log(2*2)2*2*2*3)
=a-1/((3/2)+1/(2log(2)3))
=a-2/(3+log(2)3)
=a-2/(3+((3a-2)/(1-a)))
=3a-2
log(a)b表示以a为底b的对数