If x is a positive real number different from unity such that `2log_bx = log_ax + log_cx,` then prove that `c^2 = (ca)^(log_ab)`,

If x is a positive real number different from unity such that 2log_(b)x=log_(a)x+log_(c)x then prove that c^(2)=(ca)^(log_(a)b)

If x is a positive real number different from 1 such that log_a x, log_b x, log_c x are in A.P then

If x is a positive real number different from 1 such that log_a x, log_b x, log_c x are in A.P then

If x is a positive real number different from 1 such that log_a x, log_b x, log_c x are in A.P then

If x is a positive real number different from 1 such that log_(a)x,log_(b)x,log_(c)x are in A.P then

If x is a positive real number different from 1 such that log_(a)^(x),log_(b)^(x),log_(c)^(x) are in A.P , then

If X is a positive real number other than 1 such that log_(a)x.log_(b)x,log_(c)x are in A.P. then

If a, b, c are distinct positive real numbers each different from unity such that (log_b a.log_c a -log_a a) + (log_a b.log_c b-logb_ b) + (log_a c.log_b c - log_c c) = 0, then prove that abc = 1.

Let a and b be real numbers greater than 1 for which there exists a positive real number c, different from 1, such that 2(log_a c +log_b c)=9log_ab c . Find the largest possible value of log_a b .

Let a and b be real numbers greater than 1 for which there exists a positive real number c, different from 1, such that 2(log_a c +log_b c)=9log_ab c . Find the largest possible value of log_a b .