PLS HELP URGENT !!!!

Question

If log_m(ab) = 4 and log_m(a/b) = 12, then find log_m(a)/log_mb

thank you.

Answer 1

log(ab) = 4 = loga + logb

log(a/b) = 12=loga -logb add to eliminate one variable

16 =2loga

loga = 16/2 =8

log(a) = 8

logb =loga-12= 8-12= -4

log(b) =-4

loga/logb= 8/-4 = -2

logm(a)/logm(b) = -2

(the base could be m or any other base)