Show that log₂ w = 2log₄ w

Hence solve the simultaneous equations

log₄ t² - log₂ u² = (log_0.5 9)-1

4^t = 2^u-2

Thanks

To answer the first part, try raising both sides of the equation to the power of 2.

yeah i got that part, that was quite easy but the second part is pretty tricky

Here's a hint. All the following are simplifications from the original problem

2log₄ t-2log₄ u² =log_1/2 9-1
2log₄ (t/u² )=log_1/2 9-1
log₄ (t/u² )=log_1/2 3-1/2
2t/u² =4^{log_1/2 3}

Now just relate t to u from the second equation and substitute in.

Brad

I totally agree, at the moment there is nothing at all to stop people from posting as anonymous, plus it is not discouraged in any of the policy statements or in the introductions to the subject areas, so no-one can be blamed for posting as anonymous. I'm not sure it's possible to make posting anonymous impossible and the AskNRICH team wouldn't be able to anyway...

It is rather a moot point as AFAICT they don't bother to check if you are who you say you are when you sign up.

For what it's worth I think each poster should have a unique identifier, even if it isn't their real name. Apart from anything else it makes it easier to see what's going on when 2 anonymous people are posting. I'm assuming it would be a fairly trivial task to prevent anonymous posting.

It is possible - and I've just done it...

Like Brad said, I don't see any harm in anonymous posting even in these sections (besides the kind of post that the anonymous above made, which doesn't exactly set a friendly tone). If someone wanted to remain anonymous, couldn't they simply sign up for a second NRICH account?

Olof

P.S. I'm not the anonymous from above either :)

But what's the point? Is anyone that embarrassed about their ability/inability in mathematics? And you can still ask the statue of anonymous if you really are. In anon's defence, I'm not entirely sure the comment (that doesn't set the friendly tone) came out how it was intended.

Personally I don't have any problems posting using my name, but obviously some people do, and I don't see that there is any harm in it - so why remove the option?

I thought the comment by anonymous was simply a light-hearted throwaway line, certainly not to be taken literally.

And no, I'm not the anonymous either :-)

And yes, I really think it is better giving at least some sort of name, rather than posting as anonymous. Otherwise it makes the responder feel as if (s)he is talking into a vacuum, whereas if a name is given, it makes it feel like communicating with someone, somewhere. And like Oliver says, there is still a section for anonymous posting, so if anyone has some reason for not giving their name, (s)he can still post to the board. But as I say above, no-one who has posted anonymously previously can be blamed in any way.

Well, there are 2 main objection to posting as anonymous:

1. The askNRICH team will have no idea of what level of maths you have experienced.

2. As Michael have said, it makes us feel like we are talking to a brick wall/vacuum or suchlike.

I am not blaming people who post anonymously, but I think the comment above was insulting (even if it wasn't intended). You will not get what you want by throwing insulting comments on others. Personally, I perceive posts by anonymous as sending out the 'I don't care' signal so such messages have the lowest priority. It may take a long time before I would consider answering those questions.

Hopefully we could see some new names appearing on the board....

Kerwin

Nothing like a good non-Maths related discussion. There hasn't been one in a while :). Shame this one was so short though. J

Olof

Sheesh...you guys.
just to make the point...
feel free to delete this persona.
:)

As a matter of form, this was posted by none of the above. In no way do I associate myself with the comments of any other persons anonymous, nor indeed with any poetry that they may have written.

Anon.

LOL :)