MathematicsIf a x =b, b y =c   and xyz=1  , then what is the value of c z   ?

If a x =b, b y =c   and xyz=1  , then what is the value of c z   ?


  1. A
    z
  2. B
    b
  3. C
    a
  4. D
    c 

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    Solution:

    Given that,
    a x =b.(i) b y =c..(ii)  
    Taking log on both sides of equations given below,  Equation (i) becomes,  log a x =logb xloga=logb    x= logb loga (iii)   Equation (ii) becomes,
    log b y =logc ylogb=logc   y= logc logb (iv)  
    Substituting the values of x   and y   in xyz=1  
    We get,
    logb loga × logc logb ×z=1 logc loga ×z=1 z×logc=loga  
    log c z =loga.(v)  
    Find the value of c z   ,
    Apply formula 3,
    c z = e loga  
    We know that,
    e loga =a    Then,
    c z =a   Hence, the value of c z   is a.
    Therefore, option 3 is correct.
     
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