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" 9."log_(e)x^(2)

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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

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

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

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If f(x)=|{:(2^(-x),e^(x log_(e)2),x^(2)),(2^(-3x),e^(3x log_(e)2),x^(4)),(2^(-5x),e^(5x log_(e)2),1):}| then show that f(x) is symmetric about origin

If x^(y) = e^(x - y) prove that (dy)/(dx) = (log_(e)x)/((1 + log_(e)x)^(2)) .

Find the value of lim_(xto0^(+)) (3(log_(e)x)^(2)+5log_(e)x+6)/(1+(log_(e)x)^(2)).

Find the value of lim_(xto0^(+)) (3(log_(e)x)^(2)+5log_(e)x+6)/(1+(log_(e)x)^(2)).

Find the value of lim_(xto0^(+)) (3(log_(e)x)^(2)+5log_(e)x+6)/(1+(log_(e)x)^(2)).

If log_(e) (x^(4) y) = a and log_(e) (x^(2) y^(2)) = b, then log_(e) sqrt(y) in terms of a and b is