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Okay, this may be an easy question for most A-Level students but i’m only 13 ok:colondollar:

9^(3x-6) = (1/3)^y

Find an equation for y

Use your answer to solve these simultaneous equations:
9^(3x-6) = (1/3)^y
and
y = 2x + 4

Pls help idgi
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Reply 2
Avatar for Notnek
Notnek
21
Original post by frankielogue
Okay, this may be an easy question for most A-Level students but i’m only 13 ok:colondollar:

9^(3x-6) = (1/3)^y

Find an equation for y

Use your answer to solve these simultaneous equations:
9^(3x-6) = (1/3)^y
and
y = 2x + 4

Pls help idgi

Try to make both sides have the same base

e.g.if you had this:

8x=42x+1\displaystyle 8^x = 4^{2x+1}

⇒(23)x=(22)2x+1\Rightarrow \left(2^3\right)^x = \left(2^2\right)^{2x+1}

⇒23x=24x+2\Rightarrow 2^{3x} = 2^{4x+2}

⇒3x=4x+2\Rightarrow 3x = 4x+2


Yours is harder than this example but see if you can use a similar method. Post your working/thoughts if you get stuck.
(edited 7 years ago)
Original post by notnek
Try to make both sides have the same base

e.g.if you had this:

8x=42x+1\displaystyle 8^x = 4^{2x+1}

⇒(23)x=(22)2x+1\Rightarrow \left(2^3\right)^x = \left(2^2\right)^{2x+1}

⇒23x=24x+2\Rightarrow 2^{3x} = 2^{4x+2}

⇒3x=4x+2\Rightarrow 3x = 4x+2


Yours is harder than this example but see if you can use a similar method. Post your working/thoughts if you get stuck.


Not sure if this is 100% correct but I got

(32)3x−6=(3−1)y\displaystyle (3^2)^{3x-6} = (3^-1)^y

Unparseable latex formula:

\Rightarrow \left 3^{6x-12} = -y



Is this correct?
(edited 7 years ago)
Reply 4
Avatar for Notnek
Notnek
21
Original post by frankielogue
Not sure if this is 100% correct but I got

(32)3x−6=(3−1)y\displaystyle (3^2)^{3x-6} = (3^-1)^y

Unparseable latex formula:

\Rightarrow \left 3^{6x-12} = -y



Is this correct?

I don't know if you've finished editing your latex but you've made a mistake in changing (3−1)y(3^{-1})^y into −y-y. The 33 has disappeared.

You should use 'preview post' before posting to check your latex looks okay.
Original post by notnek
I don't know if you've finished editing your latex but you've made a mistake in changing (3−1)y(3^{-1})^y into −y-y. The 33 has disappeared.

You should use 'preview post' before posting to check your latex looks okay.


isn’t -1 * y = -y?
Reply 6
Avatar for Notnek
Notnek
21
Original post by frankielogue
isn’t -1 * y = -y?

It is but your 33 has disappeared. Correct version:

(3−1)y=3(−1×y)=3−y\left(3^{-1}\right)^y = 3^{ \left( -1 \times y\right) } = 3^{-y}
Original post by notnek
It is but your 33 has disappeared. Correct version:

(3−1)y=3(−1×y)=3−y\left(3^{-1}\right)^y = 3^{ \left( -1 \times y\right) } = 3^{-y}


Ohhh I see😂 Do you then solve :
6x−12=−y\displaystyle 6x-12 = -y
to get the answer for y? this was my main problem - not sure what to do next
Reply 8
Avatar for Notnek
Notnek
21
Original post by frankielogue
Ohhh I see😂 Do you then solve :
6x−12=−y\displaystyle 6x-12 = -y
to get the answer for y? this was my main problem - not sure what to do next

The question wants you to find an equation for y in terms of x. You just need to divide both sides by -1 and then you're done.

If you had already reached this point when you asked this question then you should have posted all your working at the start.
Original post by notnek
The question wants you to find an equation for y in terms of x. You just need to divide both sides by -1 and then you're done.

If you had already reached this point when you asked this question then you should have posted all your working at the start.


My bad. I see that but I don’t get the simultaneous equations part.
Reply 10
Avatar for Notnek
Notnek
21
Original post by frankielogue
My bad. I see that but I don’t get the simultaneous equations part.

You've changed 9^(3x-6) = (1/3)^y into a simple linear equation. So now you have two linear equations which you can solve in the normal way.
Reply 11
Avatar for WRK
WRK
11
Original post by frankielogue
Okay, this may be an easy question for most A-Level students but i’m only 13 ok:colondollar:

9^(3x-6) = (1/3)^y

Find an equation for y

Use your answer to solve these simultaneous equations:
9^(3x-6) = (1/3)^y
and
y = 2x + 4

Pls help idgi


A-level Mathematics actually scares me. So glad i won't have to take it.
Original post by notnek
You've changed 9^(3x-6) = (1/3)^y into a simple linear equation. So now you have two linear equations which you can solve in the normal way.


No you have to solve these equations:
9^(3x-6) = (1/3)^y
2x + 4


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