Home
Class 12
MATHS
If a^x=b, b^y=c,c^z=a then the value of ...

If `a^x=b, b^y=c,c^z=a` then the value of xyz is

Text Solution

Verified by Experts

`a^(x)=b,b^(y)=c,c^(z)=a`
`rArr" "x=log_(a)b,y=log_(b)c,z=log_(c)a`
`rArr" "xyz=(log_(a)^(b))(log_(b)^( c))(log_(c)^(a))=(logb)/(loga)(logc)/(logb)(loga)/(logc)=1`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 1.35|1 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 1.36|1 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE PUBLICATION|Exercise ILLUSTRATION 1.33|1 Videos

  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE PUBLICATION|Exercise Subjective Type|9 Videos

  • MATHMETICAL REASONING

    CENGAGE PUBLICATION|Exercise Archives|10 Videos

Similar Questions

Explore conceptually related problems

If a^x=b,b^y =c,c^z=a , find the value of xyz.

If a^(x)=b,b^(y)=c,c^(z)=a show that xyz =1 (a,b,c positive numbers)

Knowledge Check

  • If (x-a)//(b+c) + (y-b)//(c+a)+(x-c)//(a+b) = 3 then the value of x is

    A
    abc
    B
    1/(abc)
    C
    a+b+c
    D
    1/(a+b+c)

  • If a,b,c are in G. P. and x, y are A.M. of a, b and b, c respectively, then the value of ((a)/(x)+ (c )/(y)) is-

    A
    1
    B
    2
    C
    0
    D
    4

    • Similar Questions

    Explore conceptually related problems

    If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, b ,c-z],[ a-x, b-y, c]|=0, then the value of the expression a/x+b/y+c/z is a. 0 b. -1 c. 1 d. 2

    If u=ax+by+cz , v=ay+bz+cx , w=az+bx+cy , then the value of |{:(a,b,c),(b,c,a),(c,a,b):}|xx|{:(x,y,z),(y,z,x),(z,x,y):}| is

    Given a=x//(y-z), b=y//(z-x), and c=z//(x-y),w h e r e .x , y and z are not all zero, then the value of a b+b c+c a is a. 0 b. 1 c. -1"" d. none of these

    Let x,y,z in R^(+) and 2xy+3yz+4xz=18 . If alpha , beta and gamma be the values of x , y and z respectively, for which xyz attains its maximum value, then the value of 2alpha+beta+gamma= (a) 4 (b) 6 (c) 8 (d) 12

    If x = y = 222 and z = 223, then find the value of x^(3)+y^(3)+z^(3)-3xyz

    If x + y + z = xyz and x, y, z gt 0 , then find the value of tan^(-1) x + tan^(-1) y + tan^(-1) z

    Home
    Profile