Show that if `log_b a=c` and `log_y b=c` , then

`log_a y=c^-2` .

### 1 Answer | Add Yours

`log_b a = c`

`log_y b = c`

`==> log_a y= c^-2`

We know that: `log_a b= (log_c b)/(log_c a)`

`` `log_a y=( log_b y)/(log_b a)= (log_b y)/C .........(1)`

`log_b y = (log_y y)/(log_y b) = 1/C .........(2)`

Now we will subsitute (2) into (1).

`==gt log_a y= (1/c)/c= 1/c^2 = c^-2 `

`==gt log_a y= c^-2`

``

### Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes