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Solving Equations Containing Indices

So the question was:

Solve for xx
6x36x−2\frac{6^x}{36^x{^-2}} = = 6\sqrt 6

Can someone help me with this question?
The minus 2 in the fraction is part of the power
(edited 8 years ago)

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What you want to do in this case is get all of the terms in the same base, with a power. You would end up with this:

6x62(x−2)=612(∗)\frac{6^{x}}{6^{2(x-2)}}= 6^\frac{1}{2} (*)

Then, you need to use the laws of indices to simplify this into an equation where you can equate the powers, can you see where to go from (∗)(*) ?
Original post by ozmo19
So the question was:

Solve for xx
6x36x−2\frac{6^x}{36^x{^-2}} = = 6\sqrt 6

Can someone help me with this question?
The minus 2 in the fraction is part of the power


Write 36 as 626^2?
Reply 3
Avatar for ozmo19
ozmo19
OP
16
Original post by Jordan\
What you want to do in this case is get all of the terms in the same base, with a power. You would end up with this:

6x62(x−2)=612(∗)\frac{6^{x}}{6^{2(x-2)}}= 6^\frac{1}{2} (*)

Then, you need to use the laws of indices to simplify this into an equation where you can equate the powers, can you see where to go from (∗)(*) ?


Original post by Mr M
Write 36 as 626^2?


Ive gotten to the part where the bases are the same with a power and i am left with this:

6x6^x==
Unparseable latex formula:

(6^{1/2})(6^2)^x^{-2}



Where do i go from here?
(edited 8 years ago)
Original post by ozmo19
Ive gotten to the part where the bases are the same with a power and i am left with this:

6x6^x==
Unparseable latex formula:

(6^2)^x^{-2}



Where do i go from here?

Now what you need to do is use the equation that I left you with (∗)(*) and using the subtraction rule of indicted you need to simplify the left hand side of the equation so you have both sides as 6 to the power of something.

At this point you can just equation the powers and solve for xx

What you have there is correct, but how would you simplify the right hand side (to bring all of the powers together?)
(edited 8 years ago)
Reply 5
Avatar for ozmo19
ozmo19
OP
16
Original post by Jordan\
Now what you need to do is use the equation that I left you with (∗)(*) and using the subtraction rule of indicted you need to simplify the left hand side of the equation so you have both sides as 6 to the power of something.

At this point you can just equation the powers and solve for xx

What you have there is correct, but how would you simplify the right hand side (to bring all of the powers together?)


i updated my post, look at it again
I had already gotten there but didn't know what to do next
Original post by ozmo19
So the question was:

Solve for xx
6x36x−2\frac{6^x}{36^x{^-2}} = = 6\sqrt 6

Can someone help me with this question?
The minus 2 in the fraction is part of the power


Are you allowed a calculator to solve this?
Reply 7
Avatar for ozmo19
ozmo19
OP
16
Original post by Jordan\

What you have there is correct, but how would you simplify the right hand side (to bring all of the powers together?)


Unparseable latex formula:

(6^{2})^x^{-2}



this can be simplified to 6 to the power of 2x-4 but how do i multiply that 1/2 (the other power)?
The book i am using says simplifying this part comes to 6 to the power of 2x-7/2 but i don't understand this
(edited 8 years ago)
Reply 8
Avatar for poohat
poohat
18
The simplest way to do it would (from the original equation) be to just take the logarithm of both sides, and use the fact that log(a/b^c) = log a - c log b

The equation then becomes:

x log(6) - (x-2)log(36) = 1/2 log(6)

and you can solve directly from there
Reply 9
Avatar for ozmo19
ozmo19
OP
16
Original post by Eux
Are you allowed a calculator to solve this?


No, it's C1
Original post by ozmo19
No, it's C1


What course is this, as logs normally come up in c2, and logs are usually the way to solve these
Reply 11
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ozmo19
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16
Original post by Eux
What course is this, as logs normally come up in c2, and logs are usually the way to solve these


CCEA is the exam board..
Original post by ozmo19
i updated my post, look at it again
I had already gotten there but didn't know what to do next

On the right hand side you have two terms multiplied together, what you need to do is add the powers of these to simplify them to one term, i.e

6x=612∗62(x−2) 6^{x} = 6^\frac{1}{2} * 6^{2(x-2)}
6x=612+2(x−2) 6^{x} = 6^{\frac{1}{2} + 2(x-2)}
6x=612+2x−4 6^{x} = 6^{\frac{1}{2} + 2x - 4}
6x=62x−72 6^{x} = 6^{2x -\frac{7}{2}}

Does that help?
Original post by ozmo19
CCEA is the exam board..

I do CCEA too, I actually remember doing this question :lol:
Reply 14
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ozmo19
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Original post by Jordan\
I do CCEA too, I actually remember doing this question :lol:


There was me trying the multiply the powers, this is what happens when you haven't don't any maths in months... thanks for the help:tongue:
Original post by ozmo19
Unparseable latex formula:

(6^{2})^x^{-2}



this can be simplified to 6 to the power of 2x-4 but how do i multiply that 1/2 (the other power)?
The book i am using says simplifying this part comes to 6 to the power of 2x-7/2 but i don't understand this

This is one of the rules of indices, if you had 2∗22 * 2 you could also write it as 21∗212^1 * 2^1 so when simplifying this we add the powers together to get 222^2, as if we had just multiplied them together we would still have 212^1 and we know that the answer should be 2∗2=222 * 2 = 2^2

We can also do this with much higher powers, so 334∗93=334∗32(3)=332∗36=3383^{34} *9^{3} = 3^{34} * 3^{2(3)} = 3^{32} * 3^6 = 3^{38}
Original post by ozmo19
There was me trying the multiply the powers, this is what happens when you haven't don't any maths in months... thanks for the help:tongue:

No problem, I know the feeling :lol:
can't you put 6x = t ? and 36x = t2


so it becomes t = 60.5 ( t2 - 2 ) and then treat it like a quadratic? discriminant btw is positive 47 :-)
i mean 49
ops...i missed the part when you said the -2 is part of the power :-O

sorry

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