Simplify `(log_(a)b^(4)-log_(c)a^(4))/(log_(b)c^(2)-log_(c)a^(2))`

a^(log_(b)c)=c^(log_(b)a)

Simplify: (1)/(1+log_(a)bc)+(1)/(1+log_(b)ca)+(1)/(1+log_(c)ab)

(1+log_(c)a)log_(a)x*log_(b)c=log_(b)x log_(a)x

The expression ((log_((a)/(b))p)^(2)+(log_((b)/(c))p)^(2)+(log_((a)/(a))p)^(2))/(((log_((a)/(b))p+log_((b)/(c))p+log_((c)/(a))p))^(2)) wherever defined,simplifies to

If a,b,c are distinct real number different from 1 such that (log_(b)a. log_(c)a-log_(a)a) + (log_(a)b.log_(c)b.log_(c)b-log_(b)b) +(log_(a)c.log_(b)c-log_(c)C)=0 , then abc is equal to

log_(e^(2))^(a^(b))*log_(a^(3))^(b^(c))log_(b^(4))^(e^(a))

If log_(a)b+log_(b)c+log_(c)a vanishes where a, b and c are positive reals different than unity then the value of (log_(a)b)^(3) + (log_(b)c)^(3) + (log_(c)a)^(3) is

If the equation (log_(12)(log_(8)(log_(4)x)))/(log_(5)(log_(4)(log_(y)(log_(2)x))))=0 has a solution for 'x' when c lt y lt b, y ne a , where 'b' is as large as possible, then the value of (a+b+c) is equals to :

4.Prove that log_(a)(bc).log_(b)(ca).log_(c)(ab)=2+log_(a)(bc)+log_(b)(ca)+log_(c)(ab)