Quadratics more....

If the eqn [ log12 (log8 (log4x)) ] / [log5(log4(logy(log2x))))] = 0

has a solution for 'x' when c<y<b , y≠a , where 'b' is as large as possible & 'c' is as smal as

possible , then the value of (a+b+c) =

(A)18

(B)19

(C)20

(D)21l

3 Answers

23
qwerty ·

(1)see here for a solution of x , only the numerator can be zero
so u get x = 216

(2) now denominator cant be =0

so we get the condition that x≠2y4 ...(i)

now one value of x we know is 216

so from (i) 216 ≠2y4

so y4≠16

so y≠2

so a = 2....(1)

(3) now in the denominator

log4(logy(log2x))) > 0

so x > 2y

we kno 1 value of x i.e 216

this x also satisfies above ineq

so 216 > 2y

so 16 > y

so b = 16...(2)

but i m confused here that from prop of log y≠1 and above i got that y≠2

so wat will be a =?

23
qwerty ·

with bipin sirs help we can safely say a = 2

bcz they want that value of y wich y cannot take btween b and c

bcz if it wasnt the case then we would hav said that a can also be 20 or something

4
UTTARA ·

Thanks QWERTY

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