设56a=14，试用a表示log756，log756=（式子中不得出现对数）．

Question

设56 ^a =14，试用a表示log ₇ 56，log ₇ 56=______（式子中不得出现对数）．

Answer 1

(5 6a)/(2) =7，则log ₇ (5 6a)/(2) =1
即log ₇ 56 ^a -log ₇ 2=1
即alog ₇ 56-log ₇ 2=1，
即a（log ₇ 7+log ₇ 8）-log ₇ 2=1
得log ₇ 2= (1-a)/(3a-1)
log ₇ 56=1+3log ₇ 2=1+ (3-3a)/(3a-1) = (2)/(3a-1)
故答案为： (2)/(3a-1)