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

If a,b,c are distinct positive real numbers each different from unity such that (log_(a)a.log_(c)a-log_(a)a)+(log_(a)b*log_(c)b-log b_(b))+(log_(a)c.log_(a)c-log_(c)c)=0 then prove that abc=1

log_(x rarr n)-log_(a)y=a,log_(a)y-log_(a)z=b,log_(a)z-log_(a)x=c

If x,y,z are in G.P.nad a^(x)=b^(y)=c^(z), then log_(b)a=log_(a)c b.log_(c)b=log_(a)c c.log_(b)a=log_(c)b d.none of these

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

Q.If log_(x)a,a^((x)/(2)) and log_(b)x are in G.P.then x is equal to (1)log_(a)(log_(b)a)(2)log_(a)(log_(e)a)+log_(a)log_(b)b(3)-log_(a)(log_(a)b)(4) none of these

Let a,b" and "c are distinct positive numbers,none of them is equal to unity such that log _(b)a .log_(c)a+log_(a)b*log_(c)b+log_(a)c*log_(b)c-log_(b)a sqrt(a)*log_(sqrt(c))b^(1/3)*log_(a)c^(3)=0, then the value of abc is -

Prove that: log_(a)x xx log_(b)y=log_(b)x xx log_(a)y

log_(a)a*log_(c)a+log_(c)b*log_(a)b+log_(a)c*log_(b)c=3 (where a,b,c are different positive real nu then find the value of abc.

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

If x,y,z are in G.P.and a^(x)=b^(y)=c^(z), then (a) log ba=log_(a)c(b)log_(c)b=log_(a)c(c)log_(b)a=log_(c)b(d) none of these