If x = 9 is one of the solutions of ` log_(e)(x^(2)+15a^(2))-log_(e)(a-2)=log_(e)((8ax)/(a-2))`,then

Options

A. ` a= 3/5`
B. a = 3
C. x = 15
D. x = 2

Answer

B

Explanation

`log_(e)(x^(2)+15a^(2))-log_(e)(a-2)=log_(e)((8ax)/(a-2))`
Here` a gt 2, (8ax)/(a-2) gt 0`
`:. x gt 0`
Now` (x^(2)+15a^(2))/(a-2) = (8ax)/(a-2)`
` or x^(2) = 8ax+15a^(2) = 0`
` rArr x = 3a, 5a`
Now, ` x = 9`
` rArr a = 3, 9/5`
But ` a gt 2`
` :. a = 3`
For ` a = 3, x = 9, 15`