Need help. Brain is fuzzy.

Nobody Special:

I know that I know how to do this problem, but for some reason it's not coming out right. Could someone show me how to do this?
I have the answer, I just forgot how to get to it.

lg2 (4 - 3x) = 5

Many thanks! ^_^

Hi Special It is really good to see you here again.
I think that you want
log ₂(4-3x) = 5 [ that is, log base 2 of (4-3x) = 5 ]

There is a couple of different ways to think about this

If log _ba = x
then a=b ^x
Remember: A log is a power. That is a really important thing to keep in your mind.
If you rearrange your equation like this it should become easy.

Method 2.
This uses log identities
If
y=log ₃x
then you can solve it like this (I am have trouble finding the right words so I will just show you0
3 ^y= 3 ^log₃x

the 3 and the log base 3 cancel each other out so you are left with
3 ^y= x

The two methods are really the same. Just different ways to think about it. You should be comfortable with both.
I haven't answered your question exactly but have I given you enough information?
If you get stuck please post again.

and again, it is really good that you are back.

Thank you so much, Melody!

If you wouldn't mind, I have another question:

If a and b are nonzero real numbers and (2.41)^a=(6.95)^b , what is (b/a)^2 ?

I've looked back through the book over and over again and the answer book doesn't help either. I'm not sure what a problem like this is called so I can't google it or anything, lol.
I know it's winter break, but could you help?? ^_^

no one gives a c**p about your stupid question

Taylortrojan57 - Behave yourself. If you are not going to be nice then you are not welcome in this forum!

Hi special,
I haven't actually done your question but if you just take the log of both sides it shouldn't be too difficult.

this is a list of log identities that I often refer to, you will need to use the 3rd one in the main list.
http://en.wikipedia.org/wiki/List_of_logarithmic_identities

It is not winter break for me. It is summer. I'm in Sydney, Australia. Public schools don't break up till next week but the kids won't be doing any work now. (I'm not a kid)
Once they break up they don't go back till February. I like answering all your questions all the time. I like it when you help other people too.
I believe Professor Harlod never actually existed. I think the Lopez girls were playing a game. They didn't mean any harm. They are a fun bunch of young people but I am glad that they killed off that particular Professor.

Yeah, I had a feeling the professor was a bit over-done. But it was really convincing!

What base number should I use with the log? 2.41, maybe? I suppose that would get the 'a' by itself, is that the way to go?

You get b/a by itself and then square the answer i think.

It doen't matter what base you use. If you don't approximate the answer you don't even need to specify the base. But I would use base e or base 10 and get an approximation off the calculator. Remember, I haven't actually done this question yet.