15.已知等比数列{an}\{a_{n}\}{an}的各项均为正数,其前nnn项和为SnS_{n}Sn,且32Sn+1=anan+1\frac{3}{2}{S_n}+1=\sqrt{{a_n}{a_{n+1}}}23Sn+1=anan+1.(1)求{an}\{a_{n}\}{an}的通项公式;(2)若存在正整数mmm,使得log2a2m=log2am+2024\log _{2}a_{2m}=\log _{2}a_{m}+2024log2a2m=log2am+2024成立,求mmm的值.