[Math] Need help with logarithms

[Einherjar Silberio]

Hiyall.

Got a very important test (second and last chance for my math final after failing it the first time...) tomorrow and I have very limited knowledge... one thing that keeps bugging me are logarithms and there are a bunch of things on google but I'd really find it more helpful if some kind, generous soul here could help so I could ask back or so.

Well, I got this excersize in my math book which goes something like:

For an exponential model y = f(x) = C * a^x means that f(0) = 2 and f(1) = 3.
Decide f(2)

(Rough translation from Swedish... Hope it's understandable.)
Would that just mean that f(2) = C * a^2 or did I miss something?

Another kind of problem that keeps bugging me are those that look like this:

A) 2 * 10^x = 48

And:

B) 10^2x = 50

In the case of A) it's the 2 that confuses me, and in B) it's the 2x.

I would really, really appriciate if someone could kind of explain to me step by step, like you'd explain to a fruit. I am completely and utterly useless when it comes to math and I'm also very slow.

Thanks in forehand, lads.

[Asheekay]

Let me try:

I hope you know what a^x means. It means multiply a with itself for x times. Like this:
a^0 = 1 [its a rule. anything ^0 =1]
a^1 = a [means a one time]
a^2 = a * a [means a two times]
a^3 = a*a*a [means a three times]
a^4 = a*a*a*a[means a four times]
and so on

Now lets see your problem:

f(x) = C*a^x

we now know what a^x means, all that is new here is that we have to multiply the result with C.

Now lets try finding out what is C and a.

f(0) = 2

This means C*a^0 = 2

As we know from above a^0=1 [ANYTHING ^ 0 = 1. Its a universal law or something]

Ok so lets replace a^0 with 1 in the equation.

f(0) = C*a^0
=C*1
=C

Fine. Now a good thing is that they have told us that f(0)=2

This means that C = 2

Ok. Now lets use this value of C for further use:

f(1) = 2*a^1
=2*a
=2a

They have again told us that f(1)=3
Means 2a=3
means a=3/2
means a=1.5

ok. Now we know the values of both a and C. It should become easy now

f(2) = 2*1.5^3
=2*1.5*1.5
=2*2.25
=4.5
Thats the answer.

I understand that it will be very hard for you to learn it in so short a time as one day but do give it your best try.

If you do understand what i have posted, just pm me. I'd give you my msn id so you can talk directly and communicate easier.

Plus, goodluck with the test. May God help you in your time of weakness. Ameen.

[Einherjar Silberio]

Thank you so much!!

I had gone through that in school some time ago but never really understood it, but I did have a base knowledge... Just needed a small kick to get forth.

Thanks again.

[Asheekay]

Anytime man.

Feel free to post any other any day.

Its always a reptile to help a fellow reptile

[Asheekay]

Also about these type of problems:

A) 2 * 10^x = 48
And:
B) 10^2x = 50

Lets see what they mean.
For the first one:
2*10^x=48

this means that 2, when multiplied with 10^x, makes 48

this definitely means that 10^x = 24

implies x=log(10) 24

Here, we used the rule that if y^x = z

then x = z log (y)

Now lets see the next question.

10^2x=50

This means that 10, when multiplied with ITSELF 2x times, makes 50

means 2x = log(10) 50

finally x = [log(10) 50]/2

[Einherjar Silberio]

Thanks once again.

But unfortunately and as always, it turned out to be another of those moments where all I had studied was pretty much useless... A bunch of questions that I had no idea whatsoever about. Maybe a few.

Nothing with algorithms also... God, I hate everything right now xD

But thanks, mate, I really appreciate your help.

[Asheekay]

It always happens like that in exams.
As a rule, always, as in ALWAYS, practice with the questions you find hardest. That way, there will be nothing more left for you to study or fear.

[Skanker]

Just got to logarithms in my college algebra class today.
It came really quickly and easily, actually. Weird how some math makes perfect sense to some people and absolutely no sense to others, vice versa.

[Kalessin]

Many people receive an awful maths education anyway. How and whether it's explained to you by people who know what they're doing and can put it in terms you understand while giving you some insight into the underlying meaning of it makes all the difference in the world.

[Master Lindale Mustaparta]

And some people like me are just incapable of understanding this nonsense anyway. I mean really; there is NO WAY a letter can be a number. It is not possible, and it CANNOT happen.