Home
Class 12
MATHS
If a^x=b ,\ b^y=c\ a n d\ c^z=a , prove ...

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

Text Solution

Verified by Experts

We have, `a^(xyz)=(a^(x))^(yz)`
`rArr a^(xyz)=(b)^(yz)[ :' a^(x)=b]`
`rArr a^(xyz)=(b^(y))^(z)`
`rArr a^(xyz)=c^(z) [ :'b^(y)=c]`
`rArr a^(xyz)=a[ :' c^(z)=a]`
`:. A^(xyz)=a^(1)`
`rArr xyz=1`
Promotional Banner

Topper's Solved these Questions

  • BASIC MATHS

    ALLEN|Exercise Exercise(O-1)|15 Videos

  • BASIC MATHS

    ALLEN|Exercise Exercise(S-1)|10 Videos

  • APPLICATION OF DERIVATIVES

    ALLEN|Exercise All Questions|1 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    ALLEN|Exercise All Questions|1 Videos

Similar Questions

Explore conceptually related problems

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

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

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 a^x=b^y=c^z and a,b,c are in G.P. show that 1/x,1/y,1/z are in A.P.

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

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

If a,b,c,d are in GP and a^x=b^y=c^z=d^u , then x ,y,z,u are in

Prove that the line x=a y+b ,\ z=c y+d\ a n d\ x=a^(prime)y+b^(prime),\ z=c^(prime)y+d^(prime) are perpendicular if aa^(prime) + c c^(prime) + 1=0