Question

2^x=b,2^y=ab,2^z=a^2b,试说明2y=x+2

Answer 1

将指数换成对数, 得x=log2 b, y=log2 ab, z=log2 a^2b

所以 2y=2log2 ab=y=log2 a^2b^2

x+z=log2 b +log2 a^2b =log2 ba^2b=log2 a^2b^2

所以 2y=x+z

注：log 后的2为对数的底数