log以2为底20的对数减去log以4为底25的对数

Question

如题所述

Answer 1

log2 (20)-log4 (25)
=log2 (5*4) -log2^2 (5^2)
=log2 (5)+log2 (4)-log2 (5)
=log2 (2^2)
=2追问

log2^2 (5^2)如何计算到log2 (5)？

追答

log2^2 (5^2)
=lg5^2 / lg2^2
=2lg5 / 2lg2
=lg5 / lg2
=log2 (5)

一定要记到，底数的指数提出来作分母，真数的指数提出来作分子

举个列子
loga^b (c^d)
=d/b loga (c)

Answer 2

log₂20-log₄25=log₂(4×5)-log₂25/log₂4=log₂4+log₂5-2(log₂5)/2=log₂4=2

Answer 3

log4 25=log2^2 25=1/2log2 25=log2 5
这样两个对数的底相同
因此，log2 20-log2 5=log2 4=2