log a^(2)-3(b-c)^(2)

The minimum value of 'c' such that log_(b)(a^(log_(2)b))=log_(a)(b^(log_(2)b)) and log_(a) (c-(b-a)^(2))=3 , where a, b in N is :

The minimum value of 'c' such that log_(b)(a^(log_(2)b))=log_(a)(b^(log_(2)b)) and log_(a) (c-(b-a)^(2))=3 , where a, b in N is :

If log(a+b+c) = log a + log b + log c , then prove that log ((2a)/(1-a^(2))+(2b)/(1-b^(2))+(2c)/(1-c^(2))) = log(2a)/(1-a^(2)) + log (2b)/(1-b^(2)) + log(2c)/(1-c^(2)) .

Simplify log(a^(2)times b^(3))-log((a^(3))/(b^(2)))

(log x)/(2a+3b-5c)=(log y)/(2b+3c-5a)=(log z)/(2c=3a-5b')

log((a^(3)*b^(3))/(c^(3)))+log((b^(3)*c^(3))/(d^(3)))+log((c^(3)*d^(3))/(a^(3)))-3log(b^(2)c)

log((a^(3)*b^(3))/(c^(3)))+log((b^(3)*c^(3))/(d^(3)))+log((c^(3)*d^(3))/(a^(3)))-3log(b^(2)c)

log (a^(2)/b)+log(a^(4)/b^(3)) + log (a^(6)/b^(3))+…… +log ((a^(2n))/b^(n))=?

a,b,c are positive real numbers such that log a(b-c)=(log b)/(c-a)=(log c)/(a-b) then prove that (1)a^(b+c)+b^(c+a)+c(a+b)>=3(2)a^(a)+b^(b)+c^(c)>=3

int_(0)^( pi/2)(cos x)/((2+sin x)(1+sin x))dx equals (a)log((2)/(3))(b)log((3)/(2))(c)log((3)/(4))(d)log((4)/(3))