• Congratulations to the Class of 2024 on your results!
    Let us know how you went here
    Got a question about your uni preferences? Ask us here

question (1 Viewer)

?

  • ?

    Votes: 1 7.7%
  • ?

    Votes: 2 15.4%
  • ?

    Votes: 3 23.1%
  • ? sorry

    Votes: 7 53.8%

  • Total voters
    13

Xu

dangerous driver
Joined
Oct 4, 2003
Messages
52
Gender
Female
HSC
N/A
Please help me. i know this is easy, but i cant do it!!

note: log_2 means a base 2

the sum of the first 10 terms of the sereis log_2(1/x) + log_2(1/x^2) + log_2(1/x^3) +... for x>0 is -440. find that vulue of x.
 

Antisocial

Member
Joined
Oct 2, 2003
Messages
50
Hahaha, nice poll. :D ;)
I will do this question as I am typing (need to practise series and sequences, anyway).

Test to see if AP or GP, ie. T2 - T1 = T3 - T2.

T2 - T1 = log_2 (1/x) - log_2 (1/x)

Hmm. Remember subtraction of two logs is division...

log_2 (1/x / 1/x) = log_2 (1/x)

Bring the bottom denominator up top, and simplify. Then we work on...

T3 - T2 = log_2 (1/x / 1/x) = log_2 (1/x)

log_2 (1/x) = T2 - T1 = T3 - T2

Therefore it's an AP. Some forward movement now. :cool:

It says sum of 10 terms is -440. So, sum of AP.. sn = n/2 [a + (n-1)d].

-440 = 10/2 [2log_x (1/x) + (10 - 1)log_2 (1/x)]

Expand and simplify...

10log_2 (1/x) + 45log_2 (1/x) = -440

Take out HCF...

log_2 (1/x) [10 + 45] = -440

Solve for x.

log_2 (1/x) = -440 / 55

log_2x = 8

x = 2^8
x = 256

That... took longer than expected. :eek:
Hope that's the right answer.
 

Jumbo Cactuar

Argentous Fingers
Joined
Sep 8, 2003
Messages
425
Gender
Male
HSC
2003
this is a way better solution ...

-440 = log_2 (1/x) + ... + log_2 (1/x^10)
= log_2 ((1/x) * ... * (1/x^10))
= log_2 (1/x^55)
2^-440 = 1/x^55
2^440 = x^55

x = 2^(440/55) = 256
 

Xu

dangerous driver
Joined
Oct 4, 2003
Messages
52
Gender
Female
HSC
N/A
Originally posted by Jumbo Cactuar
this is a way better solution ...

-440 = log_2 (1/x) + ... + log_2 (1/x^10)
= log_2 ((1/x) * ... * (1/x^10))
= log_2 (1/x^55)
2^-440 = 1/x^55
2^440 = x^55

x = 2^(440/55) = 256
hi, sorry its me again. umm.. could soemone please explain to me who dumbo cactar got his/her (sorry) answer?

sorry.
 

hereSIR

New Member
Joined
Aug 11, 2003
Messages
11
Gender
Male
HSC
1998
RHS=log_2 (1/x) + ... + log_2 (1/x^10)
= log_2 ((1/x) * ... * (1/x^10)) (Log Rule-"the addition rule thing")

Now (1/x) * ... * (1/x^10) = (1/x^55) (Index Law - when multiply we add the powers, i.e 1+2+3......+10 = 55)
Hence the rest! (I think :p).
 

Jumbo Cactuar

Argentous Fingers
Joined
Sep 8, 2003
Messages
425
Gender
Male
HSC
2003
Originally posted by Xu
dumbo
fsss the outrage!!!

Well that is the last time I help a fellow ffviii enthusistast, or someone who coincidentally has the name of one of the characters :(
 

ssssonicyouth

phonic booth
Joined
Oct 5, 2003
Messages
199
Location
room 237
Gender
Male
HSC
N/A
Originally posted by Jumbo Cactuar
this is a way better solution ...

yes, but u missed so many lines working it was pretty pointless to use it as an attempt to explain something to xu
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top