If `y^2=x z and a^x=b^y=c^z ,` then prove that `(log)_ab=(log)_bc`

If y^(2)=xz and a^(x)=b^(y)=c^(z), then prove that (log)_(a)b=(log)_(b)c

If x,y,z are in G.P. and a^x= b^y=c^z , prove that log_b a. log_b 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 x^(2)+y^(2)=z^(2) , then prove that 1/(log_(z-y)x) + 1/(log_(z+y)x) = 2 .

if x^(2) + y^(2) = z^(2) then prove that log_(y)(z+x) + log_(y) (z-x)=2

If a,b,c are in A.P and x,y,z are in G.P prove that (b-c) logx+(c-a) log y+(a-b) log z=0

If x,y,z are in HP, then show that log(x+z)+log(x+z-2y)=2 log (x-z)

If x,y,z are in HP, then show that log(x+z)+log(x+z-2y)=2 log (x-z)

If (log x)/(b-c) = (log y)/(c-a) = (log z)/(a-b) , then prove that x^(b^2+bc+c^2).y^(c^2+ca+a^2).z^(a^2+ab+b^2)=1