On and on and on

[anthropos]

Here's a maths question I have found in a maths test. Solve for x.

 

Give me some hints please...I am clueless. Anyway ignore those green squares.

[Dave]

I believe you can solve it by saying that:

 

[math]2^x = 3 \sqrt{3\sqrt{3\sqrt{3 \dots}}} = 3 \sqrt{2^x}[/math].

 

Haven't done one of these in a while though, so I could be wrong

[Primarygun]

My method is to express the right hand side with the base 3.

Then using [Math] log [/Math] can find the answer.

Dave, don't worry, you always get the right answer.

[Primarygun]

Yours is a good method. There is a similar problem using your method to figure the solution in my local mathematical olympiad

[anthropos]

Thanks everybody!

[Dave]

It's a pretty standard way of dealing with things like continued fractions and nested things in general. You'll still need logs to get the answer, which I think is [math]x = \frac{\log 3}{\log 2}[/math].

[anthropos]

Thanks guys, you rock!

 

Anyway, I am really poor at solving questions on logarithms. I need more practice!

[anthropos]

AHA!!! I finally understand what's going on because we got back our papers and our dear teacher explained to us why! Aha, he was kind of frustrated because we only understood what was going on during his third attempt of explanation. Anyway, thanks Dave!

[Dave]

Not a problem.

[Primarygun]

AHA!!! I finally understand what's going on because we got back our papers and our dear teacher explained to us why! Aha, he was kind of frustrated because we only understood what was going on during his third attempt of explanation. Anyway, thanks Dave!

__________________

So you did understand him or you've already learnt the solution before his speaking?

[anthropos]

I mean at first I sent a message to Dave saying I don't understand, then later I seemed to grasp it (and not really at that same time...that ambiguity was horrible) and later with my teacher's aid, I totally grasp it!