" (i) "(log_(b)a)(log_(c)b)(log_(a)c)=1

Show that log_(b)a log_(c)b log_(a)c=1

If a,b,c gt1 then Delta=|(log_(a)(abc),log_(a)b,log_(a)c),(log_b(abc),1,log_(b)c),(log_(c)(abc),log_(c)b,1)| equals

( Prove that )/(1+log_(b)a+log_(b)c)+(1)/(1+log_(c)a+log_(c)b)+(1)/(1+log_(a)b+log_(a)c)=1

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

If a > 0, c > 0, b = sqrt(ac), ac != 1 and N > 0 , then prove that (log_(a)N)/(log_(c )N) = (log_(a)N - log_(b)N)/(log_(b)N - log_(c )N) .

If a, b, c are distinct positive numbers each being different from 1 such that (log_(b)a.log_(c)a-log_(a)a)+(log_(a)b.log_(c)b-log_(b)b) +(log_(a)c.log_(b)c-log_(c)c)=0 , then abc is a)0 b)e c)1 d)2

Find the values : (log_(a)b)xx(log_(b)c)xx(log_(c )d)xx(log_(d)a)

If in a right angle triangle,a and b are the length of the sides and and c is the length of the hypotenuse and c-b!=1,c+b!=1 then show that log_(c+b)(a)+log_(c-b)(a)=2log_(c+b)(a)log_(c-b)(a)

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