对数运算问题(7^lg20)*[(1/2)^lg0.7]也就是7的lg20次幂乘以1/2的lg0.7次幂

Question

对数运算问题
(7^lg20)*[(1/2)^lg0.7]
也就是7的lg20次幂乘以1/2的lg0.7次幂

Answer 1

(7^lg20)*[(1/2)^lg0.7]
=(7^lg20)/(2^lg0.7)
=[7^(lg4+lg5)]/[2^(lg7-lg10)]
=[7^(lg2+lg2+lg5)]/[2^(lg7-lg2-lg5)]
=7^lg2*7^lg2*7^lg5/2^lg7*2^lg2*2^lg5
=(7^lg2/2^lg7)*(7^lg2*2^lg2)*(7^lg5*2^lg5)
=1*14^lg2*14^lg5
=14^(lg2+lg5)
=14^lg10
=14^1
=14
注：其中有一步 7^lg2/2^lg7=1 ,证明如下：
即证 7^lg2=2^lg7
取对数： lg(7^lg2)=lg(2^lg7)
即证 lg2*lg7=lg7*lg2 ,这是显然的.