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C3 expo and log functions help please

I am hoping someone might be able to help as i am really stuck on the question below

Solve, giving your answers to 2 decimal places, the equation

3[In(2x)]^3 - 4[In(2x)]^2 - 5In(2x) + 2 = 0

any help much appreciated.

thanks

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Reply 1
That equation remid you of anything? A polynomial?
Reply 2
Sorry - I'm still confused! I did C1 and C2 around 2008 so not sure if it was in there and I can't remember?


have reviewed the answer to see if that helps, but the working goes to


[In(2x)+1] [3In(2x) -1] [in(2x)-2] and i have no idea how to get from the first equation to the second.
Reply 3
Original post by Catful1
Sorry - I'm still confused! I did C1 and C2 around 2008 so not sure if it was in there and I can't remember?


have reviewed the answer to see if that helps, but the working goes to


[In(2x)+1] [3In(2x) -1] [in(2x)-2] and i have no idea how to get from the first equation to the second.


Could you solve

3y34y25y+2=03y^3 - 4y^2 - 5y + 2 = 0
Reply 4
I'm still coming up blank! I know I know how to do it, I just can't remember, and I don't have my old books to look it up :frown:
Reply 5
you can try inputting the cubic equation into your calculator which will solve it for you
Reply 6
or you could find one factor(when the remainder=0)by guessing and do long division to find the other two factors
Reply 7
substitute ln2x with y and solve for y. After you have found the factors substitute y back with ln2x and solve for x
(edited 10 years ago)
Here's a starting point:

Divide the whole thing by ln2x.
Now set ln2x=x and sub x into the equation.
See the quadratic..?

Hope that helps.

Posted from TSR Mobile
Reply 9
Original post by TenOfThem
Could you solve

3y34y25y+2=03y^3 - 4y^2 - 5y + 2 = 0



Original post by Catful1
I'm still coming up blank! I know I know how to do it, I just can't remember, and I don't have my old books to look it up :frown:


Are you not doing C3/C4 now

Have you not covered the factor theorem
Original post by Pessimisterious
Here's a starting point:

Divide the whole thing by ln2x.
Now set ln2x=x and sub x into the equation.
See the quadratic..?

Hope that helps.

Posted from TSR Mobile


This does not give a quadratic, it is not appropriate advice
Reply 11
Am there now - once i realised the correct formula it was straight forward! Thanks for all your help
Original post by TenOfThem
This does not give a quadratic, it is not appropriate advice


My bad, hah, I didn't see the +2 at the end.
Reply 13
Original post by TenOfThem
Could you solve

3y34y25y+2=03y^3 - 4y^2 - 5y + 2 = 0

When you factories the cubic polynomial the equation will be (y-2)(3y-1)(y+1)=0
Original post by Jafar70
When you factories the cubic polynomial the equation will be (y-2)(3y-1)(y+1)=0


Which leads to the solution that the OP had seen
Reply 15
Original post by TenOfThem
Which leads to the solution that the OP had seen


so by sub in ln2x for y to solve x. I got x= 3.69, 0.70, 1.36 (to 2.d.p). Is that right?
(edited 10 years ago)
Original post by Jafar70
so by sub in ln2x for y to solve x. I got x= 3.69, 0.70, 1.36 (to 2.d.p). Is that right?


yes
Original post by AH244
you can try inputting the cubic equation into your calculator which will solve it for you



WTF how do you do that?????
Original post by Lord Frieza
WTF how do you do that?????


depends on your calculator
Reply 19
Original post by Lord Frieza
WTF how do you do that?????

i dont know about all calculators but the casio fx 991ES can do it for quadratic and cubic equations, saves a lot of time

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