Bucket's Questions

[bucket]

ahhhhh, interesting way of doing that :p
thanks alot man

[Collin Li]

Hm... it's pretty standard. A more clever approach (less 'hack at the problem' method) would be to recognise that 3 and 9 are related by a power of 2, although it's all the same:











Since , or by taking the of both sides:



Or maybe you think it's strange because I didn't bring the denominator to the RHS? Meh, haha, whatever works for you - the operations you do will be essentially the same.

[bucket]

eh
Solve

I'm getting and it says the answer is

what am I doing wrong? lol

[bec]

yay I can do this one!

So first you need to make sure everything has the same base: 2.
This gives:

Now, remembering your exponential rules, you can ADD the powers on the LHS.
This gives:

Lastly, equate the powers. (What you're doing here is taking the log base 2 of everything)
This gives:






hope that helps!

[bucket]

ah... stupid little errors on my part (N)
thanks alot bec!

[bucket]

Ok I have another one....


The answer is 0, -2

[Neobeo]

Let

[bucket]

eh.
I dont understand where 0 and -2 come from.

[Toothpaste]

We know that and using the null factor theorem.

substituting in gives:
  and
= 1 therefore
= therefore **

**
change of base law

[bucket]

ohh, thanks heaps man.

[bucket]

Simplify .

Ack, I don't know what to do when faced with two different bases lol.

[dcc]

well, (since )

so another way of writing this would be:



since

then, just continuing as you normally would, adding and dividing as necessary:

[bucket]

mm.
the question says 'simplify without using a calculator' (i didn't write it coz i didn't think it would be relevant =\)
and the answer is 9?
I'm assuming it solved for x.......?

[dcc]

Which is as far as that one will go

[bucket]

mm... i don't know how it gets 9