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Show that if   `log_b a=c`  and  `log_y b=c`  , then `log_a y=c^-2` .

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lbawa | Student, Undergraduate | eNoter

Posted December 9, 2011 at 5:15 AM via web

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

`log_a y=c^-2` .

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted December 9, 2011 at 7:44 AM (Answer #1)

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`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`

``

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