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# Solving with indices

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1. Solving with indices
Below is a question which I need help on:

Solve the following equation:

I do understand that 81 must be set as x to the power of y. Also I understand that the 32 must be set to the same value of x (same) to the power of z (different):

How do I get the value for x?? How do I know the value for x??

Thanks a lot for any help provided.
2. Re: Solving with indices
Are you allowed to use logs?
3. Re: Solving with indices
Use logs?

If you cannot use logs for any reason then notice that n must be negative. How do you get from 16 to 32 using powers? (both are powers of 2). Same question for 81 to 243? Can you guess at a value for n now?
4. Re: Solving with indices
I have no knowledge of logs yet.
5. Re: Solving with indices
(Original post by james22)
Use logs?

If you cannot use logs for any reason then notice that n must be negative. How do you get from 16 to 32 using powers? (both are powers of 2). Same question for 81 to 243? Can you guess at a value for n now?
16 -->32 is denominater (first fraction) -->numerator (second fraction)

Are you really allowed to do this????????? Or are you doing it becasuse you somehow know that n is negative?
6. Re: Solving with indices
why are you assuming n is negative??
7. Re: Solving with indices
It may make it simpler for you if you write each number as a product of primes:

This should give you a clue as to why the power is negative and lead you to the solution.
8. Re: Solving with indices
(Original post by notnek)
It may make it simpler for you if you write each number as a product of primes:

This should give you a clue as to why the power is negative and lead you to the solution.
But the numerator of the first fraction is not equal to the numerator of the second fraction. How do I deal with this problem?
9. Re: Solving with indices
(Original post by krisshP)
But the numerator of the first fraction is not equal to the numerator of the second fraction. How do I deal with this problem?
so try flipping them and adjusting the power accordingly...

Last edited by Plato's Trousers; 06-07-2012 at 11:48.
10. Re: Solving with indices
btw if a power is negative, don't you usually put the number as a fraction with 1 as the numerator?
11. Re: Solving with indices
(Original post by krisshP)
btw if a power is negative, don't you usually put the number as a fraction with 1 as the numerator?
see my post #9 - get it now?
12. Re: Solving with indices
(Original post by krisshP)
16 -->32 is denominater (first fraction) -->numerator (second fraction)

Are you really allowed to do this????????? Or are you doing it becasuse you somehow know that n is negative?
I know n is negative because you cannot (easily) get from the numerator of the first to the numerator of the second fraction. However this is much easier if the first fraction is flipped. If n is negative the fraction is flipped so i assumed that n is negative because it makes things easier.
13. Re: Solving with indices
ok. I got the correct answer of n=-1.25.

Thanks a lot for making me learn

14. Re: Solving with indices
yes. I get it.
15. Re: Solving with indices
(Original post by krisshP)
ok. I got the correct answer of n=-1.25.

Thanks a lot for making me learn

it's better not to use decimals for indices. use
16. Re: Solving with indices
ok plato's trousers

Thanks
17. Re: Solving with indices
(Original post by krisshP)
ok plato's trousers

Thanks
It's just easier to see what's going on if you use a fractional index. The top number is the power and the bottom number is the root.

So, for example

Last edited by Plato's Trousers; 06-07-2012 at 11:59.
18. Re: Solving with indices
(Original post by krisshP)
btw if a power is negative, don't you usually put the number as a fraction with 1 as the numerator?
You probably already got this by now, but just to clarify:

The degenerate case is when b=1:

Alternatively, we can start by assuming the degenerate case to be true (since you accepted that):

Thus, as the degenerate case holds true:

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Last updated: July 6, 2012
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