If `a^x=c^q=b` and `c^y=a^z=d` then prove that, `xy = qz`

Similar Questions

Explore conceptually related problems

If a^x=b ,\ b^y=c\ a n d\ c^z=a , prove that x y z=1

If a^x=b^y=c^z\ a n d\ b^2=a c , prove that y=(2x z)/(x+z)

If a^x=b^y=c^z and b^2=a c , then show that y=(2z x)/(z+x)

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

If x=1+(log)_a b c ,\ y=1+(log)_b c a\ a n d\ z=1+(log)_c a b ,\ then prove that x y z=x y+y z+z xdot

If a,b,c,d be in G.P. and a^x=b^y=c^z=d^w , prove that 1/x,1/y,1/z,1/w are in A.P.

If x^(a) = y^(b) = z^ (c ) and y^(2) = xz, prove that b= ( 2ac)/( a+c)

If x,y and z are in A.P ax,by and cz in G.P and a, b, c in H.P then prove that x/z+z/x=a/c+c/a

If a^((1)/(x))= b^((1)/(y))= c^((1)/(z)) and a,b,c are in G.P., prove that x,y,z are in A.P.

If a=x y^(p-1),\ b=x y^(q-1) and c=x y^(r-1) , prove that a^(q-r)b^(r-p)\ c^(p-q)=1