thank you so much for your response,actually rearragning the terms to find 'b' gives me 3logb = 2loga - 5 {upon subtracting 5 from both the sides}.
this is where i need help.please look into my partial fractions problems as well if you got the time.
Can you make x the subject of this equation: log(x)+3=2t ? In other words, if the equation log(x)+3=2t is always satisfied, what does x equal?
And I will look at the partial fractions, but I'd like to concentrate on this first.
Actually, what is your definition of a logarithm?
The last time we had a conversation I asked you some questions to assess your level of knowledge and you never answered them:
http://news.ycombinator.com/item?id=1107996
It seems to me looking over other times you've asked questions that you claim you want to get into math, and you probably think you're doing lots of stuff, but in reality I've seen no evidence of you actually trying things.
Gaining skills is a matter of spending the time. In math in particular, if you haven't spent ages getting loads of wrong answers then you won't have any real intuition as to what to do. You need loads of wrong answers, from which you can start to identify "good wrong answers". From those good wrong answers you can build an intuition as to what might work, and you can start to find excellent wrong answers.
Then the moment comes when you see how to convert an excellent wrong answer into a right answer.
With practice this becomes second nature, and after a time you wonder why you ever found it difficult. But until you've put in the hours of practice, it doesn't happen.
People think doing math is a matter of somehow finding the right process and then following it. "Tell me what to do" is the perpetual cry.
You need to try stuff. Try re-arranging the equations repeatedly into different forms until, maybe, one looks familiar. Don't just stare at stuff hoping inspiration will strike, and don't think there's a magic formula for finding the right next step.
That's not how it works.
So tell me, how many different ways can you rearrange the equation: log(x)+3=2t ?
by the way the only definition of logarithm that i know is 'log is inverse of exponents'
OK, here are some terms to simplify. In each case, what is a simpler way to write the expression:
x^3 * x^5
(t^3)^2
u^(3^2)
(g+2)^2
(z-3)^3
t^3 * t^3 = t^6
i guess it's u^6
g^2+4g+4
not sure abt (z-3)^3
expanding (z-3)^3
could it be: (z-3).(z+3)^2 ??
=>(z-3) (z^2+3z+9)
So (g+2)^2 is equal to g^2+4g+4, but it's also equal to (g+2).(g+2) [where I've used the dot for multiplication]
Does that help you for (z-3)^3 ??
here it is:x=10^y
subtract 10^y from both the sides
x-10^y=0
now subtract x from both the sides
-10^y = -x
divide by -1
-10^y/-1 = -x/-1
= 10^y = x
take log base 10 both sides
log10^y = logx
= ylog10=logx
y = logx/log10
The first part you go from x=10^y to -10^y=-x to 10^y=x. Is it not clear that if x=10^y then 10^y=x? The point is that any time A=B, then B=A.
Next, you have ended with y=log(x)/log(10). If the logarithms are base 10, what is log(10)? Can you use that to make your result simpler?
Next question: if t=log(u) (where the logarithm is base 10) then what does u equal?
i'am assuming this would end up in some number called 'e' which i came accross somewhere in the past.please help..i'am not sure what that number means and how to get it
The simple rules are these:
log(a.b) = log(a) + log(b)
hence
log(a^4) = log(a.a.a.a) = log(a)+log(a)+log(a)+log(a) = 4.log(a)
Therefore
if a = b^z
then log(a) = log(b^z)
so log(a) = z.log(b)
log_b(b) = 1 : Log (base b) of b is 1.
Hence log_b(b^2) = 2
log_b(b^3) = 3
and so on.
if x = b^y
then log_b(x) = log_b(b^y)
= y.log_b(b)
= y
If a = 10^b
then log(a) = log(10^b)
= b.log(10)
= b.1
= b
Finally, you need to study sections 1, 2 and 3 of this page:
http://en.wikipedia.org/wiki/Logarithm
What's on that page will also help you to understand the questions.
http://www.phon.ucl.ac.uk/cgi-bin/wtutor?tutorial=t-log
Work through that - it will help with your basic understanding of what's going on.
Have you not tried searching for tutorials?
If y=log(x) (with 10 as the base of the logarithms) then what does x equal in terms of y?
This is not the medium for teaching you about the basic, basic, basic rules of elementary algebra. There are loads of tutorials on the web - try using Google to search for tutorials on logarithms.
When you tell me what you've searched for, and what the first rules are that they give you, then I'll start helping again.