If `x >1 and log_2 x,log_3 x,log_x 16` are in GP, then what is x equal to ?

Options

A. 9
B. 8
C. 4
D. 2

Answer

A

Explanation

`log_(2)x,log_(3)x,log_(x)16` are in G.P.
`:.(log_(3)x)/(log_(2)x)=(log_(x)16)/(log_(3)x)`
`implies(log_(3)x)^(2)=log_(2)x.logx16`
`implies2xxlog_(3)x=log2x.logx2^(4)`
`implies2xxlog_(3)x=4xxlog_(2)x.log_(x)2`
`implieslog_(3)x=2(log_(2)x xxlog_(x)2)`
`implieslog_(3)x=2[(log_(2)x)/(log_(2)x)]" "(becauselog_(b)a=(1)/(log_(a)b))`
`implieslog_(3)x=2impliesx=3^(3)=9`