HSC 2015 Maths Marathon (archive) (1 Viewer)

[rand_althor]

Re: HSC 2015 2U Marathon

If 2f(x)+3f(-x)=15-4x, find f(x).

 

[astroman]

Re: HSC 2015 2U Marathon

3^2x+2.3^x-15=0
my brain is dead and can't think someone remind me how to do this plz lel.

 

[kawaiipotato]

Re: HSC 2015 2U Marathon

Let y = 3^x
Eqn turns into y^2 + 2y - 15 = 0
Solve as a quadratic for y
And then equate to 3^x
Reject any negative y values by noting that 3^x > 0 for all real x

 

[astroman]

Re: HSC 2015 2U Marathon

Let y = 3^x
Eqn turns into y^2 + 2y - 15 = 0
Solve as a quadratic for y
And then equate to 3^x
Reject any negative y values by noting that 3^x > 0 for all real x

ty

 

[astroman]

Re: HSC 2015 2U Marathon

Let y = 3^x
Eqn turns into y^2 + 2y - 15 = 0
Solve as a quadratic for y
And then equate to 3^x
Reject any negative y values by noting that 3^x > 0 for all real x

wait what happened to the 2.3?

 

[Flop21]

Re: HSC 2015 2U Marathon

Let y = 3^x
Eqn turns into y^2 + 2y - 15 = 0
Solve as a quadratic for y
And then equate to 3^x
Reject any negative y values by noting that 3^x > 0 for all real x

Why would 2.3^x = 2y? Wouldn't that make it 2*3^x, which would = 6^x ??

 

[astroman]

Re: HSC 2015 2U Marathon

Why would 2.3^x = 2y? Wouldn't that make it 2*3^x, which would = 6^x ??

same, i think there is a different way of solving these.

 

[Flop21]

Re: HSC 2015 2U Marathon

same, i think there is a different way of solving these.

I'm trying right now different ways, but the 2.3 is stuffing me up.

Do you know the answer??


EDIT: With these questions you usually either do what above poster said (use say 'm' to make it easier), or take the log / ln of both sides, or turn the exponential into a log equation instead if possible.

 

[astroman]

Re: HSC 2015 2U Marathon

yea answer is 1

 

[nisak]

Re: HSC 2015 2U Marathon

let y = 3^x

y^2+2y-15=0

(y-3)(y+5) =0
y=3 and y=-5

3^x=3
therefore x=1

and 3^x=-5
no solution

so x=1

 

[VBN2470]

Re: HSC 2015 2U Marathon

. Note that the term actually means .

 

[Flop21]

Re: HSC 2015 2U Marathon

. Note that the term actually means .

I don't understand why it would mean that? I understand "." is used as "x / multiplication" sometimes, but why doesn't it mean 2.3 (23/10)?? How are we suppose to know it means 2 * 3?

 

[astroman]

Re: HSC 2015 2U Marathon

I don't understand why it would mean that? I understand "." is used as "x / multiplication" sometimes, but why doesn't it mean 2.3 (23/10)?? How are we suppose to know it means 2 * 3?

sorry my mistake, the question has the "." in the middle not the bottom, stupid i know.

 

[Flop21]

Re: HSC 2015 2U Marathon

sorry my mistake, the question has the "." in the middle not the bottom, stupid i know.

Ooooooooh. Haha that makes sense.

Yeah I actually remember coming across a question like this and I still thought the dot in the middle was a point, not multiplication.

 

[Drsoccerball]

Re: HSC 2015 2U Marathon

 

[VBN2470]

Re: HSC 2015 2U Marathon

 

[Drsoccerball]

Re: HSC 2015 2U Marathon

I think you should've let the 2015'ers answer that one ...

 

[VBN2470]

Re: HSC 2015 2U Marathon

I think you should've let the 2015'ers answer that one ...

 

[VBN2470]

Re: HSC 2015 2U Marathon

If 2f(x)+3f(-x)=15-4x, find f(x).

 

[dan964]

Re: HSC 2015 2U Marathon

If 2f(x)+3f(-x)=15-4x, find f(x).

found it