Match the following :

Options

A. `atoi,btoii,ctoiii,d to iv`
B. `atoiii,btoiv,ctoi,d to ii`
C. `atoi,btoiv,ctoii,d to iii`
D. `atoii,btoiv,ctoii,d to i`

Answer

D

Explanation

a. We have `3/(x+8)=4/(6-x)`
`implies18-3x=4x+32implies7x=14impliesx=-2`
b. We have `(2^(x-1).4^(2x+1))/(8^(x-1))=64`
`implies(2^(x).2^(-1).4^(2x).4)/(8^(x).8^(-1))=64=1/(4^(x)).4^(2x).16=64implies4^(x)=64/16=4`
On comparing we get x=1
c. We have `4^(x)-4^(x-1)=24`
`implies4^(x)-(4^(x))/4=24implies4^(x)(1-1/4)=24implies(2^(2))^(x)=(24xx4)/3=32`
`implies2^(2x)=2^(5)`
On comparing we get `2x=5impliesx=5/2`
Now `(2x)^(x)=(5)^(5//2)`
d. We have `4^(x+1)=256`
`implies4^(x+1)=(4)^(4)`
On comparing we get `x+1=4impliesx=3`