Question

y=log8(48x^3-2x^5)+log8(x) . 8 is the base. Solve and find the sum of the natural number x values.

Answer 1

us log8(a) +log8(b)=log8(a*b)

Answer 2

And after that?

Answer 3

so than will get y=log8(x(48x^3 -2x^5)) =log8(48x^4 -2x^6)=
=log8(2x^4(24-x^2))

Answer 4

there must be some information missing - this cannot be "solved".
e.g. is the question solve for x when y=0?

Answer 5

The problem was the same I wrote, but I guess it's supposed to be y=0.

Answer 6

i thought the same. but says to " find the sum "

Answer 7

Answer is supposed to be 10.

Answer 8

use this property, log8 x = y => x = 8^y = 1 ... rest is quite easy.

Answer 9

I'm kind of stuck there, don't remember the way to solve that equation.

Answer 10

2x^6-48x^4+1=0

Answer 11

the question needs to be checked otherwise you could spend time solving the "wrong" question.

Answer 12

y=log8(48x^3-2x^5)+log8(x) . 8 is the base.Find the argument values. And then the sum of natural number solutions.

Answer 13

didn't you say ... y=0??

Answer 14

The problem given is in the form of y=log8(48x^3-2x^5)+log8(x). I suppose y might be 0?

Answer 15

ErkoT - so i think you need to check the interval where the logarithm function is defined firstly and after us this interval for this logarithm with base 8 what you have got in the last step

Answer 16

lol, you will never be able to solve it. that's a equation in x and y, that will give you are curve.

Answer 17

And now I'm officially confused.

Answer 18

???

Answer 19

Never mind with that problem, I'll put another one to the left.

Answer 20

first you need to say where one logarithm function is defined ?
can you tel me now here ?

Answer 21

I think I understand that part, but then I have no idea.

Answer 22

why ? how you have learned on your math study in your school ?

Answer 23

I'm just tired as hell and english is not my native language so it's pretty difficult to translate all of the text in both ways.

Answer 24

so if i remember correct need to be allways greater than zero ...

Answer 25

ok - I think jhonyy9 has interpreted the question correctly.
you need to find the sum of the "integer" solutions to this equation.
as jhonyy9 indicated, you first need to determine the valid range.

Answer 26

Yes, makes sense.

Answer 27

it's a very badly worded question though - kudos to jhonyy9 for getting it right!

Answer 28

camon asnaseer hope you will can make it right till the end

Answer 29

Sorry for that, not that good at translating from one language to another.

Answer 30

I would suggest you also post in original language to avoid confusion like this in the future (as others may be able to translate it better)

Answer 31

Note taken.

Answer 32

so we need to find the sum of the integer solutions to this:\[log_8(2x^4(24-x^2))>0\]

Answer 33

which can be simplified to:\[2x^4(24-x^2)\gt8^0\]or,\[2x^4(24-x^2)\gt1\]

Answer 34

And how's that one solved?

Answer 35

I'm sorry if the questions are too stupid, but I'm just overly tired and still a lot to do.

Answer 36

I think we can use this approach:\[2x^4(24-x^2)-1\gt0\]then use difference of two squares to get:\[(x^2\sqrt{2(24-x^2)}+1)(x^2\sqrt{2(24-x^2)}-1)\gt0\]

Answer 37

asnaseer - what sign ,,kudos" ?

Answer 38

jhonyy9: see here: http://en.wikipedia.org/wiki/Kudos

Answer 39

ok thank you

Answer 40

yw

Answer 41

nice very

Answer 42

So I get 48x^4-48x^6-1=0 , how to solve that one?

Answer 43

check it newly because what you have got there not is right

Answer 44

yes exactly

Answer 45

ErkoT can you solve one inegality ?

Answer 46

Yes, got the same, stupid mistake.

Answer 47

And how do you solve that one?

Answer 48

ok, so we want to solve this inequality:\[48x^4−2x^6−1\gt0\]

Answer 49

Yes.

Answer 50

and it asked for "natural" numbers - so I am guessing this implies we only want the positive x values

Answer 51

I agree.

Answer 52

ok - one way I can think of is to find the maximum value of this function and then the solutions are just all natural numbers less than or equal to this value

Answer 53

Derive it?

Answer 54

Or differentiate or I don't even know the exact word.

Answer 55

yes, differentiate to get:\[-12x^3(x^2-16)=0\]which gives us:\[x=0\]or\[x=\pm4\]

Answer 56

we need to differentiate again to find which x gives the maximum.

Answer 57

that gives:\[576x^2-60x^4\]

Answer 58

which means max is at \(x=\pm4\)so our solution must be:
x=1, 2, 3, 4
so sum = 1+2+3+4 = 10

Answer 59

I think I can't thank you enough for that one! Thanks!

Answer 60

you are more than welcome - it was a very interesting problem. I'm glad I could help and thanks to @jhonyy9 for clarifying the question in the first place.

Answer 61

@jhonyy9 , thank you!
Thank you both!

Answer 62

yw asnaseer was my pleasure

good luck

bye