Not sure if this is the way to solve , however trying is not bad.

log_bM^r=rlog_bM

log_bM^r=log_b  (M1+M2+M3...+Mr)   //m1,m2,m3 =M ; 1,2,3 represents index  

        =log_bM1+log_bM2+log_bM3+....log_bMr

M1, M2, M3 ..Mr represents same variable M there fore the next step is just arithmetic addition, i.e addition of r variable =rx

     =rlog_bM