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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: lacoste on November 06, 2008, 05:53:23 pm

Title: Just a few qsts.
Post by: lacoste on November 06, 2008, 05:53:23 pm: I'm stuck on these questions ... any help would be appreciated

1). 8^(x+1) = 4^(3x-1)/2^(2x)

2). 5^(2x)-4(5^x)-5=0

3). Find the set of values of q for which 4* 2^(0.2q) >2 ?

Cheers!!
Title: Re: Just a few qsts.
Post by: Mao on November 06, 2008, 05:56:32 pm: 1.

$2^{3x+3}=\frac{2^{6x-2}}{2^{2x}} = 2^{4x-2}$

$\implies 3x+3=4x-2$

2. let $A=5^x$

$\implies A^2-4A-5=0$

3.

$\implies 2^{0.2q+2}>2^{1}$

$\implies 0.2q+2>1$

EDIT: phail typo is phail :(
Title: Re: Just a few qsts.
Post by: nerd on November 06, 2008, 06:50:00 pm: Quote from: Mao on November 06, 2008, 05:56:32 pm
1.

$2^{3x+2}=\frac{2^{6x-2}}{2^{2x}} = 2^{4x-2}$

$\implies 3x+2=4x-2$

2. let $A=5^x$

$\implies A^2-4A-5=0$

3.

$\implies 2^{0.2q+2}>2^{1}$

$\implies 0.2q+2>1$

Umm...for question 1, I think it would be

$2^{3x+3}=\frac{2^{6x-2}}{2^{2x}} = 2^{4x-2}<br /><br />\implies 3x+3=4x-2$
Title: Re: Just a few qsts.
Post by: lacoste on November 06, 2008, 07:45:46 pm: Quote from: Mao on November 06, 2008, 05:56:32 pm
3.

$\implies 2^{0.2q+2}>2^{1}$

$\implies 0.2q+2>1$

do i solve for q? and if so, is that the only set of values (Q was "
3). Find the set of values of q for which 4* 2^(0.2q) >2 ? ")

does q=-5?
Title: Re: Just a few qsts.
Post by: Lulu on November 06, 2008, 07:50:49 pm: 0.2q + 2 >1

0.2q > -1

q > -5

that is your set of values

you can test it by putting -5 back into your equation, you'll find that it equals exactly 2, therefore any x-value above -5 will satisfy the condition $\implies 2^{0.2q+2}>2$