`a)` Đúng

Xét `a-1=log_27 5-1=log_27 5-log_27 27=log_27 (5/27)<0`

`-> a-1<0 -> a<1`

`log_27 5>0 -> 0<a<1`

`b)` Sai

`bc=log_3 7*log_2 3`

`bc=log_3 7 * 1/[log_3 2]`

`bc=[log_3 7]/[log_3 2]`

`bc=log_2 7`

`c)` Sai

`log_27 5=a`

`-> log_[3^3] 5=a`

`-> 1/3log_3 5=a`

`-> log_3 5=3a`

`log_6 45`

`= log_6 (9*5)`

`= log_6 9 +log_6 5`

`= log_6 3^2+[log_3 5]/[log_3 6]`

`= 2log_6 3+[log_3 5]/[log_3 6]`

`= 2/[log_3 6]+[log_3 5]/[log_3 6]`

`= [2+log_3 5]/[log_3 6]`

`= [2+log_3 5]/[log_3 (3*2)]`

`= [2+log_3 5]/[log_3 3+log_3 2]`

`= [2+log_3 5]/[1+1/[log_2 3]]`

`= [2+3a]/[1+1/c]`

`= [2+3a]/[[c+1]/c]`

`= [2c+3ac]/[c+1]`

`d)` Đúng

`log_6 35`

`= log_6 (7*5)`

`= log_6 7+log_6 5`

`= [log_3 7]/[log_3 6]+[log_3 5]/[log_3 6]`

`= [log_3 7+log_3 5]/[log_3 (3*2)]`

`= [log_3 7+log_3 5]/[1+log_3 2]`

`= [log_3 7+log_3 5]/[1+1/[log_2 3]]`

`= [b+3a]/[1+1/c]`

`= [b+3a]/[[c+1]/c]`

`= [bc+3ac]/[c+1]`

`= [c(b+3a)]/[c+1]`

`-> {(m=3),(n=1),(p=1):}`

`-> m^2+n^2+p^2=3^2+1^2+1^2=11`