Queries in Quantitative Aptitude

1.log x + log y = log (x + y). 

log (xy) = log (x + y). 

xy = x + y. 

xy - y = x. 

y (x - 1) = x. 

y = x / (x - 1)  Option c is correct

2. log2 x  + log4 x  + log16 x   =  21/4

log2 x  + 1/2 log2 x  +  1/4 log2 x  = 21/4

log2 x  ( 1 + 1/2 + 1/4)  =  21/4

log2 x   *   7/4   =  21/4

log2 x   =   21/4   *  4/7  =  3

 x   =  2 to the power 3  = 8.   Option a is correct

3. x  to the power 1/p  =  y to the power 1/q  =  z to the power  1/r  =  K (assumed)

x  =  K to the power p,   y = K to the power q,  z = K to the power r,

x y z  = 1,  so (K to the power p)   *  (K to the power q) * (K to the power r)  = 1.

K  to the power (p + q + r)  = 1.

p + q + r  =  0. Option b is correct.